diff --git "a/data/gnn/QA/Base/Text_Only_test.json" "b/data/gnn/QA/Base/Text_Only_test.json" --- "a/data/gnn/QA/Base/Text_Only_test.json" +++ "b/data/gnn/QA/Base/Text_Only_test.json" @@ -1,4058 +1,3 @@ -[ - { - "id": "gnn-easy-graph117", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [0,1]\nThe edges are: (5,0) (4,0) (3,0) (1,5) (6,1) (2,5) (4,5) (6,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [1,2]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,2]\nnode 6: [2,1]." - } - ] - }, - { - "id": "gnn-easy-graph9", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,1]\nThe edges are: (0,1) (0,4) (3,1) (1,2) (1,4) (2,3)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [1,4]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [0,1]." - } - ] - }, - { - "id": "gnn-easy-graph75", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [1,1]\nThe edges are: (0,3) (1,0) (4,0) (1,5) (1,2) (4,1) (5,2) (2,3) (4,2) (4,3)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,3]\nnode 1: [3,4]\nnode 2: [3,4]\nnode 3: [2,3]\nnode 4: [4,4]\nnode 5: [2,2]." - } - ] - }, - { - "id": "gnn-easy-graph17", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,1]\nThe edges are: (1,0) (1,3) (1,2) (2,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [2,1]\nnode 2: [1,2]\nnode 3: [1,1]\nnode 4: [1,0]." - } - ] - }, - { - "id": "gnn-easy-graph192", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [0,0]\nThe edges are: (0,3) (5,1) (2,1) (7,2) (5,2) (2,6) (2,4) (3,2) (3,5) (4,5) (7,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [4,3]\nnode 3: [2,1]\nnode 4: [1,1]\nnode 5: [2,1]\nnode 6: [0,0]\nnode 7: [1,1]." - } - ] - }, - { - "id": "gnn-easy-graph179", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [0,0]\nThe edges are: (0,4) (1,0) (1,2) (1,4) (6,1) (1,3) (2,4) (7,2) (6,3) (4,6) (7,5) (6,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,1]\nnode 1: [2,3]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [2,3]\nnode 5: [0,0]\nnode 6: [0,2]\nnode 7: [2,1]." - } - ] - }, - { - "id": "gnn-easy-graph130", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [0,1]\nThe edges are: (3,0) (0,6) (2,0) (5,0) (1,4) (3,2) (2,6) (2,4) (6,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [2,1]\nnode 3: [1,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [1,0]." - } - ] - }, - { - "id": "gnn-easy-graph142", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [1,0]\nThe edges are: (0,6) (2,0) (1,0) (0,3) (2,6) (2,4) (2,3) (3,6) (6,4) (4,5) (6,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [1,0]\nnode 2: [3,2]\nnode 3: [2,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [2,3]." - } - ] - }, - { - "id": "gnn-easy-graph49", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nThe edges are: (3,0) (4,0) (1,3) (2,3) (4,2)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,0]." - } - ] - }, - { - "id": "gnn-easy-graph134", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [1,0]\nThe edges are: (4,0) (2,0) (5,0) (1,2) (1,6) (4,2) (5,2) (4,3) (6,4) (5,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [2,1]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [3,2]\nnode 5: [3,1]\nnode 6: [0,1]." - } - ] - }, - { - "id": "gnn-easy-graph165", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [0,1]\nThe edges are: (6,0) (3,0) (0,5) (4,1) (1,7) (5,1) (2,4) (7,2) (4,3) (5,3) (7,4) (5,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [2,1]\nnode 2: [1,1]\nnode 3: [2,1]\nnode 4: [2,4]\nnode 5: [2,4]\nnode 6: [0,1]\nnode 7: [3,2]." - } - ] - }, - { - "id": "gnn-easy-graph53", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [1,1]\nThe edges are: (0,1) (3,0) (2,0) (5,1) (3,2) (2,5) (3,5) (4,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [1,0]." - } - ] - }, - { - "id": "gnn-easy-graph121", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [1,0]\nThe edges are: (0,4) (0,2) (0,3) (1,2) (5,1) (3,2) (6,2) (5,2)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,2]\nnode 1: [0,2]\nnode 2: [2,3]\nnode 3: [1,2]\nnode 4: [1,1]\nnode 5: [0,1]\nnode 6: [0,1]." - } - ] - }, - { - "id": "gnn-easy-graph63", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [0,0]\nThe edges are: (1,0) (5,0) (1,3) (1,4) (2,1) (4,3) (5,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,0]\nnode 1: [2,2]\nnode 2: [1,0]\nnode 3: [2,1]\nnode 4: [1,1]\nnode 5: [2,1]." - } - ] - }, - { - "id": "gnn-easy-graph10", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,0]\nThe edges are: (2,0) (0,1) (3,0) (3,2) (4,2) (4,3)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [2,2]\nnode 3: [3,1]\nnode 4: [1,1]." - } - ] - }, - { - "id": "gnn-easy-graph76", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [0,0]\nThe edges are: (1,0) (5,0) (0,2) (1,4) (1,5) (1,3) (2,5) (5,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,0]\nnode 1: [0,1]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [2,0]." - } - ] - }, - { - "id": "gnn-easy-graph127", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,1]\nnode 5: [0,0]\nnode 6: [0,1]\nThe edges are: (3,0) (0,4) (0,5) (1,4) (1,6) (1,5) (2,3) (3,4) (4,6) (4,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [1,2]\nnode 2: [1,0]\nnode 3: [3,3]\nnode 4: [2,2]\nnode 5: [2,2]\nnode 6: [1,1]." - } - ] - }, - { - "id": "gnn-easy-graph14", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [0,1]\nThe edges are: (0,2) (1,3) (2,4) (3,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [0,2]\nnode 3: [0,2]\nnode 4: [1,2]." - } - ] - }, - { - "id": "gnn-easy-graph162", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [0,1]\nThe edges are: (0,7) (0,6) (3,0) (1,7) (1,2) (7,2) (3,2) (7,3) (3,6) (4,3) (7,4) (4,6) (5,7) (6,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,3]\nnode 1: [1,1]\nnode 2: [2,2]\nnode 3: [4,3]\nnode 4: [2,3]\nnode 5: [1,2]\nnode 6: [4,3]\nnode 7: [6,3]." - } - ] - }, - { - "id": "gnn-easy-graph124", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [0,0]\nThe edges are: (3,0) (0,4) (6,0) (1,2) (4,1) (3,2) (4,5) (5,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [1,1]\nnode 2: [2,1]\nnode 3: [2,1]\nnode 4: [3,2]\nnode 5: [0,1]\nnode 6: [2,2]." - } - ] - }, - { - "id": "gnn-easy-graph79", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,1]\nThe edges are: (0,5) (4,0) (0,2) (3,0) (1,4) (1,2) (5,3) (4,3)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,2]\nnode 5: [0,1]." - } - ] - }, - { - "id": "gnn-easy-graph93", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [0,1]\nThe edges are: (0,3) (5,0) (1,3) (4,1) (1,2) (1,5) (5,2)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [1,2]\nnode 3: [2,1]\nnode 4: [1,1]\nnode 5: [2,1]." - } - ] - }, - { - "id": "gnn-easy-graph77", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,1]\nThe edges are: (5,0) (0,1) (3,0) (4,1) (2,5) (5,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,3]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [0,2]\nnode 5: [2,0]." - } - ] - }, - { - "id": "gnn-easy-graph20", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,0]\nThe edges are: (3,0) (2,1) (3,1) (4,3)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,1]\nnode 1: [0,2]\nnode 2: [1,1]\nnode 3: [3,1]\nnode 4: [0,1]." - } - ] - }, - { - "id": "gnn-easy-graph143", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [1,1]\nThe edges are: (2,0) (6,0) (3,0) (1,4) (2,6) (2,4) (3,6) (3,4) (5,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [1,0]\nnode 2: [2,1]\nnode 3: [2,1]\nnode 4: [3,2]\nnode 5: [1,0]\nnode 6: [1,1]." - } - ] - }, - { - "id": "gnn-easy-graph89", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [0,0]\nThe edges are: (5,0) (0,1) (0,3) (2,1) (4,1) (2,3) (3,5) (4,3) (5,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [2,2]\nnode 2: [1,1]\nnode 3: [2,2]\nnode 4: [1,1]\nnode 5: [2,2]." - } - ] - }, - { - "id": "gnn-easy-graph44", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,0]\nThe edges are: (4,0) (0,3) (2,0) (1,2) (2,3)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,2]\nnode 3: [2,0]\nnode 4: [1,0]." - } - ] - }, - { - "id": "gnn-easy-graph120", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,0]\nThe edges are: (0,1) (0,6) (0,2) (4,0) (1,6) (3,1) (1,4) (5,1) (2,6) (2,5) (6,4) (5,4) (5,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [1,3]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [2,1]\nnode 5: [1,2]\nnode 6: [2,3]." - } - ] - }, - { - "id": "gnn-easy-graph87", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [1,0]\nThe edges are: (0,5) (0,1) (1,3) (5,1) (2,1) (1,4) (5,2) (4,2) (3,5) (3,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [3,3]\nnode 2: [2,2]\nnode 3: [2,2]\nnode 4: [0,3]\nnode 5: [1,3]." - } - ] - }, - { - "id": "gnn-easy-graph166", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [1,0]\nThe edges are: (0,2) (0,7) (0,6) (3,1) (1,2) (5,1) (6,1) (2,5) (7,2) (3,5) (7,3) (4,7) (4,6) (7,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [2,2]\nnode 2: [4,1]\nnode 3: [3,1]\nnode 4: [1,0]\nnode 5: [3,1]\nnode 6: [3,0]\nnode 7: [4,2]." - } - ] - }, - { - "id": "gnn-easy-graph94", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [0,0]\nThe edges are: (1,0) (0,2) (5,0) (4,0) (3,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [0,1]." - } - ] - }, - { - "id": "gnn-easy-graph64", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [0,0]\nThe edges are: (2,0) (0,3) (5,0) (1,2) (3,1) (2,4) (5,3)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,0]\nnode 1: [2,0]\nnode 2: [1,3]\nnode 3: [1,2]\nnode 4: [1,0]\nnode 5: [1,1]." - } - ] - }, - { - "id": "gnn-easy-graph118", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [1,1]\nThe edges are: (0,6) (0,1) (6,1) (1,5) (2,5) (6,3) (4,3) (4,6) (4,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [1,2]\nnode 2: [0,0]\nnode 3: [1,2]\nnode 4: [1,2]\nnode 5: [1,2]\nnode 6: [0,4]." - } - ] - }, - { - "id": "gnn-easy-graph128", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [0,0]\nThe edges are: (0,6) (4,0) (3,0) (6,1) (2,1) (2,4) (2,5) (3,5) (4,5) (6,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [1,0]\nnode 2: [2,1]\nnode 3: [2,1]\nnode 4: [3,1]\nnode 5: [2,2]\nnode 6: [3,1]." - } - ] - }, - { - "id": "gnn-easy-graph30", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [0,1]\nThe edges are: (4,0) (0,1) (2,0) (1,4) (3,1) (2,3)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [2,2]\nnode 2: [2,1]\nnode 3: [1,1]\nnode 4: [2,1]." - } - ] - }, - { - "id": "gnn-easy-graph104", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [0,0]\nThe edges are: (0,3) (1,0) (0,2) (5,0) (6,0) (1,4) (5,1) (3,2) (6,2) (6,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [1,3]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,2]\nnode 6: [0,2]." - } - ] - }, - { - "id": "gnn-easy-graph119", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [0,1]\nnode 6: [0,0]\nThe edges are: (0,3) (0,5) (6,0) (0,4) (5,1) (1,6) (2,1) (4,3) (6,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [1,2]\nnode 4: [0,1]\nnode 5: [1,2]\nnode 6: [1,3]." - } - ] - }, - { - "id": "gnn-easy-graph48", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [1,0]\nThe edges are: (0,4) (3,0) (4,1) (3,1) (1,2) (2,4) (2,3)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [2,1]\nnode 3: [2,2]\nnode 4: [2,2]." - } - ] - }, - { - "id": "gnn-easy-graph19", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,1]\nThe edges are: (0,2) (1,2) (3,2) (2,4) (3,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [2,3]\nnode 3: [2,1]\nnode 4: [1,1]." - } - ] - }, - { - "id": "gnn-easy-graph1", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [1,1]\nThe edges are: (1,0) (1,4) (2,1) (3,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [1,2]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [2,1]." - } - ] - }, - { - "id": "gnn-easy-graph108", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,1]\nThe edges are: (4,0) (5,0) (0,3) (5,1) (1,3) (2,3) (4,5) (6,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [2,3]\nnode 4: [1,1]\nnode 5: [3,3]\nnode 6: [0,0]." - } - ] - }, - { - "id": "gnn-easy-graph51", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [1,1]\nThe edges are: (1,0) (4,0) (4,2) (5,3) (4,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [2,3]\nnode 5: [0,2]." - } - ] - }, - { - "id": "gnn-easy-graph157", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [0,0]\nThe edges are: (0,1) (3,0) (4,0) (7,1) (6,1) (1,3) (1,4) (7,2) (2,3) (5,2) (7,3) (4,3) (4,7) (5,4) (5,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [3,3]\nnode 2: [0,2]\nnode 3: [2,3]\nnode 4: [1,4]\nnode 5: [2,2]\nnode 6: [0,2]\nnode 7: [1,3]." - } - ] - }, - { - "id": "gnn-easy-graph145", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,1]\nThe edges are: (0,6) (4,0) (5,0) (0,2) (1,3) (5,1) (2,1) (6,3) (5,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,3]\nnode 1: [1,1]\nnode 2: [2,1]\nnode 3: [1,2]\nnode 4: [1,0]\nnode 5: [2,2]\nnode 6: [1,1]." - } - ] - }, - { - "id": "gnn-easy-graph129", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [1,1]\nThe edges are: (5,0) (1,0) (4,1) (1,6) (2,1) (1,3) (4,2) (2,6) (3,2) (3,5) (4,6) (5,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,0]\nnode 1: [3,4]\nnode 2: [3,2]\nnode 3: [2,1]\nnode 4: [3,2]\nnode 5: [2,2]\nnode 6: [2,2]." - } - ] - }, - { - "id": "gnn-easy-graph70", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,0]\nThe edges are: (0,3) (0,1) (0,2) (1,4) (3,2) (2,4) (2,5) (4,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [1,1]\nnode 2: [2,1]\nnode 3: [1,1]\nnode 4: [3,2]\nnode 5: [2,2]." - } - ] - }, - { - "id": "gnn-easy-graph122", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [0,1]\nnode 6: [0,1]\nThe edges are: (1,0) (4,1) (2,1) (5,2) (3,4) (4,5) (5,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,1]\nnode 1: [2,3]\nnode 2: [0,2]\nnode 3: [1,1]\nnode 4: [0,2]\nnode 5: [2,3]\nnode 6: [0,1]." - } - ] - }, - { - "id": "gnn-easy-graph168", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,0]\nnode 7: [0,1]\nThe edges are: (0,2) (4,0) (5,1) (1,3) (6,1) (7,1) (4,1) (7,2) (3,7) (7,4) (5,6) (5,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [3,2]\nnode 2: [0,2]\nnode 3: [0,2]\nnode 4: [0,3]\nnode 5: [1,2]\nnode 6: [0,2]\nnode 7: [3,3]." - } - ] - }, - { - "id": "gnn-easy-graph195", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [0,1]\nnode 6: [1,0]\nnode 7: [0,0]\nThe edges are: (7,0) (1,0) (3,0) (6,0) (3,1) (1,4) (7,2) (4,2) (2,6) (3,6) (7,4) (4,5) (5,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,0]\nnode 1: [1,2]\nnode 2: [2,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [2,1]\nnode 6: [1,2]\nnode 7: [2,2]." - } - ] - }, - { - "id": "gnn-easy-graph56", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,0]\nThe edges are: (0,2) (1,0) (0,4) (3,0) (1,5) (1,3) (5,2) (3,2) (4,3)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [2,2]\nnode 2: [2,2]\nnode 3: [2,2]\nnode 4: [1,2]\nnode 5: [1,1]." - } - ] - }, - { - "id": "gnn-easy-graph169", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,1]\nThe edges are: (0,1) (7,0) (5,0) (0,6) (1,3) (5,1) (2,4) (3,6) (4,3) (4,5) (6,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,3]\nnode 1: [3,2]\nnode 2: [0,1]\nnode 3: [1,2]\nnode 4: [3,4]\nnode 5: [2,1]\nnode 6: [2,2]\nnode 7: [1,0]." - } - ] - }, - { - "id": "gnn-easy-graph170", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [0,1]\nThe edges are: (6,0) (7,1) (5,1) (4,2) (2,7) (6,2) (3,4) (7,3) (3,6) (4,7) (6,4) (6,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [2,1]\nnode 5: [0,1]\nnode 6: [5,1]\nnode 7: [3,1]." - } - ] - }, - { - "id": "gnn-easy-graph0", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [0,0]\nThe edges are: (1,0) (3,0) (3,2) (3,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [2,2]\nnode 4: [0,0]." - } - ] - }, - { - "id": "gnn-easy-graph91", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [1,1]\nThe edges are: (0,2) (0,1) (0,4) (2,1) (4,1) (1,5) (4,2) (2,3) (5,2) (3,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,0]\nnode 1: [4,2]\nnode 2: [4,3]\nnode 3: [2,0]\nnode 4: [3,2]\nnode 5: [1,0]." - } - ] - }, - { - "id": "gnn-easy-graph98", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,0]\nThe edges are: (0,2) (3,0) (0,5) (1,4) (5,1) (2,4) (4,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [2,1]." - } - ] - }, - { - "id": "gnn-easy-graph182", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [0,0]\nThe edges are: (0,3) (0,5) (0,1) (6,0) (1,2) (1,3) (4,1) (2,3) (3,4) (3,7) (3,6) (4,5) (6,5) (7,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [4,2]\nnode 2: [1,1]\nnode 3: [4,2]\nnode 4: [1,1]\nnode 5: [3,1]\nnode 6: [2,1]\nnode 7: [2,2]." - } - ] - }, - { - "id": "gnn-easy-graph21", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,0]\nThe edges are: (0,4) (1,0) (3,1) (2,4) (4,3)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [2,1]\nnode 4: [1,1]." - } - ] - }, - { - "id": "gnn-easy-graph159", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [1,0]\nnode 7: [0,0]\nThe edges are: (0,7) (1,3) (1,4) (1,2) (6,2) (2,4) (2,7) (5,3) (3,6) (5,4) (6,4) (5,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,0]\nnode 1: [2,0]\nnode 2: [2,0]\nnode 3: [2,1]\nnode 4: [2,1]\nnode 5: [2,0]\nnode 6: [2,0]\nnode 7: [1,2]." - } - ] - }, - { - "id": "gnn-easy-graph172", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [1,0]\nThe edges are: (0,5) (6,0) (1,0) (4,0) (5,1) (2,5) (4,2) (3,6) (3,4) (4,5) (4,6) (7,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,3]\nnode 1: [2,1]\nnode 2: [1,2]\nnode 3: [1,2]\nnode 4: [5,4]\nnode 5: [3,2]\nnode 6: [2,2]\nnode 7: [1,1]." - } - ] - }, - { - "id": "gnn-easy-graph69", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [1,1]\nThe edges are: (0,2) (0,3) (2,1) (5,1) (1,4) (3,2) (5,3) (4,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [2,3]\nnode 2: [2,0]\nnode 3: [3,2]\nnode 4: [2,1]\nnode 5: [1,1]." - } - ] - }, - { - "id": "gnn-hard-graph774", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [0,1]\nnode 12: [0,0]\nnode 13: [1,1]\nnode 14: [0,1]\nThe edges are: (14,0) (0,2) (0,6) (0,12) (1,5) (2,1) (12,1) (2,5) (2,11) (8,2) (2,7) (5,3) (3,9) (4,6) (9,5) (6,14) (12,6) (7,9) (12,7) (9,8) (8,12) (9,11) (9,10) (10,14) (10,12) (13,14)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [9,10]\nnode 1: [6,7]\nnode 2: [1,12]\nnode 3: [4,6]\nnode 4: [1,3]\nnode 5: [5,7]\nnode 6: [6,7]\nnode 7: [8,7]\nnode 8: [8,7]\nnode 9: [1,12]\nnode 10: [9,8]\nnode 11: [5,5]\nnode 12: [1,12]\nnode 13: [3,3]\nnode 14: [1,8]." - } - ] - }, - { - "id": "gnn-hard-graph376", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [0,0]\nnode 10: [1,0]\nnode 11: [0,0]\nThe edges are: (8,0) (4,1) (2,1) (7,1) (11,2) (7,2) (2,6) (4,3) (9,3) (4,10) (5,8) (5,11) (5,9) (10,6) (8,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,1]\nnode 1: [4,2]\nnode 2: [8,2]\nnode 3: [1,2]\nnode 4: [6,4]\nnode 5: [2,2]\nnode 6: [4,2]\nnode 7: [5,3]\nnode 8: [4,0]\nnode 9: [2,1]\nnode 10: [3,1]\nnode 11: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph282", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [1,0]\nnode 10: [0,1]\nThe edges are: (0,6) (0,3) (5,0) (1,2) (9,1) (1,8) (1,5) (2,7) (2,8) (3,2) (5,2) (3,9) (4,7) (10,4) (7,5) (10,7) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,6]\nnode 1: [9,8]\nnode 2: [13,9]\nnode 3: [4,5]\nnode 4: [5,3]\nnode 5: [7,6]\nnode 6: [1,1]\nnode 7: [10,8]\nnode 8: [4,3]\nnode 9: [8,4]\nnode 10: [4,6]." - } - ] - }, - { - "id": "gnn-hard-graph780", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [1,0]\nnode 11: [1,1]\nnode 12: [0,1]\nnode 13: [0,1]\nnode 14: [1,1]\nThe edges are: (4,0) (11,0) (10,0) (0,8) (2,0) (1,9) (5,1) (2,12) (14,2) (2,5) (3,13) (3,14) (5,4) (5,11) (14,5) (11,6) (14,6) (7,10) (7,12) (11,8) (8,12) (12,10) (13,10) (10,14) (11,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [12,10]\nnode 1: [4,4]\nnode 2: [15,9]\nnode 3: [4,2]\nnode 4: [8,5]\nnode 5: [11,5]\nnode 6: [5,3]\nnode 7: [7,7]\nnode 8: [10,7]\nnode 9: [1,0]\nnode 10: [13,8]\nnode 11: [16,12]\nnode 12: [11,11]\nnode 13: [4,6]\nnode 14: [13,13]." - } - ] - }, - { - "id": "gnn-hard-graph330", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,0]\nnode 9: [1,0]\nnode 10: [1,0]\nThe edges are: (6,0) (0,7) (3,0) (2,0) (6,1) (1,3) (7,2) (2,10) (6,3) (5,3) (7,4) (6,5) (7,6) (6,8) (8,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,6]\nnode 1: [2,4]\nnode 2: [4,3]\nnode 3: [2,7]\nnode 4: [2,1]\nnode 5: [2,4]\nnode 6: [5,6]\nnode 7: [3,7]\nnode 8: [1,3]\nnode 9: [1,0]\nnode 10: [1,1]." - } - ] - }, - { - "id": "gnn-hard-graph287", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [1,0]\nnode 9: [1,1]\nnode 10: [0,0]\nThe edges are: (0,1) (1,8) (1,9) (2,5) (8,2) (4,2) (4,3) (4,7) (4,10) (4,6) (6,7) (8,6) (10,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,1]\nnode 1: [2,1]\nnode 2: [7,3]\nnode 3: [4,2]\nnode 4: [6,6]\nnode 5: [2,1]\nnode 6: [7,5]\nnode 7: [7,4]\nnode 8: [7,3]\nnode 9: [3,1]\nnode 10: [5,4]." - } - ] - }, - { - "id": "gnn-hard-graph224", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [1,0]\nThe edges are: (0,5) (6,0) (0,2) (1,8) (1,4) (2,3) (5,4) (5,8) (5,9) (7,6) (8,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [2,2]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,2]\nnode 5: [3,3]\nnode 6: [2,3]\nnode 7: [1,1]\nnode 8: [2,4]\nnode 9: [1,1]." - } - ] - }, - { - "id": "gnn-hard-graph596", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [0,1]\nnode 11: [0,1]\nnode 12: [1,0]\nThe edges are: (6,0) (0,3) (1,2) (1,6) (2,8) (4,5) (10,4) (5,11) (6,8) (6,12) (6,7) (9,6) (11,7) (11,8) (9,11) (10,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,2]\nnode 1: [3,3]\nnode 2: [2,5]\nnode 3: [1,2]\nnode 4: [0,2]\nnode 5: [3,5]\nnode 6: [3,12]\nnode 7: [5,5]\nnode 8: [5,6]\nnode 9: [5,5]\nnode 10: [3,5]\nnode 11: [1,9]\nnode 12: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph333", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [1,1]\nnode 9: [0,1]\nnode 10: [1,1]\nThe edges are: (0,5) (9,0) (7,1) (1,4) (4,2) (2,9) (2,6) (3,5) (8,4) (7,10) (9,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,4]\nnode 1: [2,4]\nnode 2: [2,6]\nnode 3: [1,1]\nnode 4: [3,2]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [2,5]\nnode 8: [1,2]\nnode 9: [2,4]\nnode 10: [1,2]." - } - ] - }, - { - "id": "gnn-hard-graph718", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [1,0]\nnode 9: [1,1]\nnode 10: [0,0]\nnode 11: [0,1]\nnode 12: [1,1]\nnode 13: [0,1]\nThe edges are: (13,0) (10,1) (2,1) (1,8) (6,1) (1,9) (2,8) (3,2) (2,6) (4,2) (7,3) (12,3) (13,3) (3,4) (9,3) (4,13) (5,10) (5,6) (10,6) (7,6) (12,6) (8,10) (11,9) (10,13) (12,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [8,7]\nnode 2: [12,12]\nnode 3: [5,11]\nnode 4: [8,7]\nnode 5: [5,3]\nnode 6: [7,7]\nnode 7: [7,6]\nnode 8: [7,4]\nnode 9: [8,7]\nnode 10: [9,7]\nnode 11: [0,2]\nnode 12: [9,8]\nnode 13: [7,11]." - } - ] - }, - { - "id": "gnn-hard-graph727", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [1,0]\nnode 10: [1,1]\nnode 11: [0,1]\nnode 12: [1,0]\nnode 13: [0,0]\nnode 14: [0,1]\nThe edges are: (8,0) (0,6) (1,11) (8,1) (9,1) (13,1) (2,5) (2,4) (3,8) (10,3) (12,3) (4,3) (4,8) (8,5) (5,6) (5,10) (14,6) (6,9) (6,12) (6,13) (7,9) (11,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,5]\nnode 1: [6,6]\nnode 2: [4,7]\nnode 3: [9,10]\nnode 4: [10,8]\nnode 5: [12,9]\nnode 6: [5,12]\nnode 7: [1,2]\nnode 8: [11,14]\nnode 9: [8,4]\nnode 10: [6,7]\nnode 11: [3,4]\nnode 12: [8,5]\nnode 13: [6,4]\nnode 14: [4,2]." - } - ] - }, - { - "id": "gnn-hard-graph700", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [1,0]\nnode 9: [1,0]\nnode 10: [1,0]\nnode 11: [0,0]\nnode 12: [0,0]\nnode 13: [0,1]\nThe edges are: (0,12) (7,0) (0,1) (5,1) (1,10) (2,12) (6,3) (9,3) (4,10) (4,6) (4,7) (4,13) (13,7) (8,13) (13,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,3]\nnode 1: [2,1]\nnode 2: [0,0]\nnode 3: [3,1]\nnode 4: [7,5]\nnode 5: [2,1]\nnode 6: [3,3]\nnode 7: [6,3]\nnode 8: [3,1]\nnode 9: [1,1]\nnode 10: [4,3]\nnode 11: [3,1]\nnode 12: [1,0]\nnode 13: [3,6]." - } - ] - }, - { - "id": "gnn-hard-graph711", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [0,1]\nnode 11: [1,0]\nnode 12: [1,1]\nnode 13: [0,0]\nThe edges are: (0,8) (0,11) (0,6) (5,1) (2,5) (2,11) (13,2) (12,3) (3,4) (10,4) (5,13) (7,5) (8,13) (8,12) (13,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,1]\nnode 1: [2,2]\nnode 2: [4,3]\nnode 3: [2,1]\nnode 4: [3,1]\nnode 5: [5,1]\nnode 6: [1,0]\nnode 7: [2,2]\nnode 8: [3,1]\nnode 9: [1,1]\nnode 10: [1,1]\nnode 11: [3,0]\nnode 12: [4,2]\nnode 13: [6,3]." - } - ] - }, - { - "id": "gnn-hard-graph724", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [0,0]\nnode 8: [1,0]\nnode 9: [0,0]\nnode 10: [0,0]\nnode 11: [1,0]\nnode 12: [1,0]\nnode 13: [1,0]\nnode 14: [1,1]\nThe edges are: (0,7) (8,0) (2,1) (1,10) (1,5) (9,2) (3,6) (9,3) (8,3) (4,7) (5,14) (8,6) (10,7) (8,7) (8,12) (14,11) (13,14)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [6,3]\nnode 1: [4,4]\nnode 2: [0,2]\nnode 3: [4,4]\nnode 4: [3,1]\nnode 5: [2,2]\nnode 6: [5,3]\nnode 7: [5,3]\nnode 8: [8,3]\nnode 9: [3,2]\nnode 10: [3,2]\nnode 11: [2,1]\nnode 12: [3,2]\nnode 13: [2,1]\nnode 14: [4,4]." - } - ] - }, - { - "id": "gnn-hard-graph695", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [1,0]\nnode 9: [1,1]\nnode 10: [1,1]\nnode 11: [1,1]\nnode 12: [0,0]\nnode 13: [1,0]\nThe edges are: (0,5) (0,1) (6,0) (1,9) (7,1) (1,4) (3,1) (9,2) (2,5) (7,2) (2,8) (3,10) (4,3) (3,6) (6,5) (12,5) (5,13) (12,6) (7,9) (10,13) (12,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,3]\nnode 1: [7,5]\nnode 2: [4,6]\nnode 3: [3,2]\nnode 4: [3,3]\nnode 5: [5,4]\nnode 6: [5,3]\nnode 7: [4,6]\nnode 8: [2,2]\nnode 9: [5,6]\nnode 10: [3,2]\nnode 11: [1,1]\nnode 12: [1,1]\nnode 13: [2,1]." - } - ] - }, - { - "id": "gnn-hard-graph587", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [0,0]\nnode 10: [0,1]\nnode 11: [0,1]\nnode 12: [1,0]\nThe edges are: (6,0) (0,7) (9,1) (1,2) (3,1) (10,1) (2,4) (2,8) (3,4) (3,12) (10,3) (11,3) (4,12) (12,5) (7,6) (12,6) (6,8) (9,8) (12,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,1]\nnode 1: [8,2]\nnode 2: [8,4]\nnode 3: [11,3]\nnode 4: [8,2]\nnode 5: [3,0]\nnode 6: [9,2]\nnode 7: [4,2]\nnode 8: [8,1]\nnode 9: [5,3]\nnode 10: [5,4]\nnode 11: [3,2]\nnode 12: [12,5]." - } - ] - }, - { - "id": "gnn-hard-graph177", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [1,1]\nThe edges are: (9,0) (1,0) (1,7) (2,3) (2,7) (3,5) (8,3) (3,7) (4,5) (8,4) (8,5) (8,6) (6,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,1]\nnode 1: [4,3]\nnode 2: [3,5]\nnode 3: [6,9]\nnode 4: [2,5]\nnode 5: [2,7]\nnode 6: [3,5]\nnode 7: [6,7]\nnode 8: [3,7]\nnode 9: [2,1]." - } - ] - }, - { - "id": "gnn-hard-graph396", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [1,0]\nnode 9: [0,0]\nnode 10: [0,0]\nnode 11: [1,1]\nThe edges are: (0,9) (6,0) (1,9) (6,1) (7,1) (1,2) (6,2) (8,2) (5,3) (5,4) (7,4) (8,4) (5,9) (6,7) (8,6) (7,11) (10,8) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [6,5]\nnode 1: [10,9]\nnode 2: [9,3]\nnode 3: [0,1]\nnode 4: [4,5]\nnode 5: [6,5]\nnode 6: [10,5]\nnode 7: [11,3]\nnode 8: [10,4]\nnode 9: [5,1]\nnode 10: [4,4]\nnode 11: [2,3]." - } - ] - }, - { - "id": "gnn-hard-graph755", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [1,0]\nnode 10: [1,0]\nnode 11: [0,1]\nnode 12: [0,1]\nnode 13: [1,1]\nnode 14: [1,1]\nThe edges are: (12,0) (2,0) (0,10) (0,8) (12,1) (2,13) (14,2) (2,3) (2,8) (3,7) (4,5) (5,10) (13,6) (11,6) (13,7) (8,12) (14,9) (10,11) (12,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [12,9]\nnode 1: [4,2]\nnode 2: [11,6]\nnode 3: [5,4]\nnode 4: [2,0]\nnode 5: [3,2]\nnode 6: [3,2]\nnode 7: [4,3]\nnode 8: [11,6]\nnode 9: [2,0]\nnode 10: [6,1]\nnode 11: [3,4]\nnode 12: [7,6]\nnode 13: [10,8]\nnode 14: [5,4]." - } - ] - }, - { - "id": "gnn-hard-graph528", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [1,0]\nnode 11: [0,1]\nnode 12: [0,0]\nThe edges are: (7,0) (5,0) (8,0) (0,9) (11,1) (5,1) (9,1) (3,2) (10,3) (4,3) (7,4) (8,4) (6,4) (12,4) (5,11) (5,9) (10,6) (6,8) (6,9) (8,7) (10,8) (9,12) (11,10) (11,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,10]\nnode 1: [6,7]\nnode 2: [1,0]\nnode 3: [0,8]\nnode 4: [5,6]\nnode 5: [4,6]\nnode 6: [4,12]\nnode 7: [2,6]\nnode 8: [2,11]\nnode 9: [3,7]\nnode 10: [6,4]\nnode 11: [2,9]\nnode 12: [4,7]." - } - ] - }, - { - "id": "gnn-hard-graph591", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [1,0]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [1,0]\nnode 12: [0,1]\nThe edges are: (12,0) (1,4) (1,2) (1,10) (12,2) (3,2) (11,2) (7,2) (2,10) (5,3) (8,3) (3,7) (6,7) (7,9) (7,11) (12,8) (9,8) (12,10) (12,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,1]\nnode 1: [8,3]\nnode 2: [17,7]\nnode 3: [10,6]\nnode 4: [2,1]\nnode 5: [3,1]\nnode 6: [3,2]\nnode 7: [13,4]\nnode 8: [10,2]\nnode 9: [4,4]\nnode 10: [12,4]\nnode 11: [13,5]\nnode 12: [10,7]." - } - ] - }, - { - "id": "gnn-hard-graph410", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [0,0]\nnode 10: [0,1]\nnode 11: [1,0]\nThe edges are: (6,0) (5,1) (1,6) (2,11) (9,3) (11,3) (7,4) (4,5) (7,5) (5,11) (6,9) (6,10) (8,6) (11,7) (10,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,3]\nnode 1: [7,6]\nnode 2: [3,2]\nnode 3: [4,3]\nnode 4: [7,5]\nnode 5: [10,8]\nnode 6: [7,7]\nnode 7: [9,7]\nnode 8: [5,4]\nnode 9: [4,3]\nnode 10: [4,5]\nnode 11: [9,5]." - } - ] - }, - { - "id": "gnn-hard-graph349", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [1,0]\nnode 10: [1,1]\nThe edges are: (0,7) (1,6) (1,9) (2,6) (2,3) (10,3) (3,8) (8,4) (5,7) (5,9) (10,7) (8,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [2,2]\nnode 2: [3,3]\nnode 3: [4,5]\nnode 4: [2,2]\nnode 5: [3,3]\nnode 6: [3,1]\nnode 7: [4,4]\nnode 8: [3,4]\nnode 9: [4,1]\nnode 10: [6,6]." - } - ] - }, - { - "id": "gnn-hard-graph389", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [1,1]\nnode 11: [0,0]\nThe edges are: (0,4) (1,0) (6,1) (2,7) (2,9) (2,11) (3,8) (10,3) (3,4) (4,7) (11,5) (6,5) (6,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,3]\nnode 1: [4,4]\nnode 2: [4,4]\nnode 3: [4,4]\nnode 4: [3,7]\nnode 5: [5,3]\nnode 6: [2,2]\nnode 7: [3,3]\nnode 8: [1,3]\nnode 9: [1,1]\nnode 10: [4,5]\nnode 11: [1,1]." - } - ] - }, - { - "id": "gnn-hard-graph801", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [1,1]\nnode 10: [0,1]\nnode 11: [0,0]\nnode 12: [0,0]\nnode 13: [1,0]\nnode 14: [0,1]\nThe edges are: (0,4) (3,0) (1,13) (5,1) (6,2) (3,8) (5,3) (12,3) (9,3) (4,7) (4,13) (4,9) (11,5) (9,5) (14,6) (6,10) (7,13) (11,7) (14,7) (12,7) (9,7) (12,8) (10,11) (10,14) (13,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [6,7]\nnode 1: [4,4]\nnode 2: [1,3]\nnode 3: [12,12]\nnode 4: [11,11]\nnode 5: [12,12]\nnode 6: [1,3]\nnode 7: [16,17]\nnode 8: [6,7]\nnode 9: [11,12]\nnode 10: [5,8]\nnode 11: [7,8]\nnode 12: [7,8]\nnode 13: [11,10]\nnode 14: [4,7]." - } - ] - }, - { - "id": "gnn-hard-graph433", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [1,0]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [1,0]\nThe edges are: (9,0) (0,5) (0,8) (1,6) (10,1) (4,2) (2,5) (7,2) (10,2) (8,2) (3,11) (3,8) (4,11) (9,5) (7,5) (5,8) (10,7) (9,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,8]\nnode 1: [3,4]\nnode 2: [12,13]\nnode 3: [5,3]\nnode 4: [5,2]\nnode 5: [11,9]\nnode 6: [1,1]\nnode 7: [8,9]\nnode 8: [11,8]\nnode 9: [7,8]\nnode 10: [6,5]\nnode 11: [4,1]." - } - ] - }, - { - "id": "gnn-hard-graph470", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [1,0]\nnode 10: [1,1]\nnode 11: [1,0]\nThe edges are: (4,0) (8,0) (0,5) (0,6) (1,9) (1,6) (2,1) (2,4) (11,2) (6,2) (3,10) (3,6) (7,4) (5,8) (5,7) (9,5) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,7]\nnode 1: [3,3]\nnode 2: [6,6]\nnode 3: [1,3]\nnode 4: [6,2]\nnode 5: [5,5]\nnode 6: [7,3]\nnode 7: [6,5]\nnode 8: [7,3]\nnode 9: [5,2]\nnode 10: [1,1]\nnode 11: [2,0]." - } - ] - }, - { - "id": "gnn-hard-graph515", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [1,0]\nnode 9: [1,0]\nnode 10: [0,0]\nnode 11: [1,1]\nnode 12: [0,0]\nThe edges are: (0,10) (0,11) (2,1) (10,1) (1,4) (2,3) (2,9) (3,7) (6,3) (3,5) (4,3) (8,3) (4,9) (11,4) (5,7) (5,12) (9,6) (7,8) (9,8) (12,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,1]\nnode 1: [7,6]\nnode 2: [8,3]\nnode 3: [8,11]\nnode 4: [10,3]\nnode 5: [5,4]\nnode 6: [6,3]\nnode 7: [4,6]\nnode 8: [7,4]\nnode 9: [7,8]\nnode 10: [3,1]\nnode 11: [5,5]\nnode 12: [2,2]." - } - ] - }, - { - "id": "gnn-hard-graph281", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [1,1]\nnode 9: [0,0]\nnode 10: [1,1]\nThe edges are: (0,4) (8,0) (0,1) (3,0) (2,4) (2,10) (8,3) (5,8) (8,6) (8,7) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,5]\nnode 1: [2,2]\nnode 2: [3,2]\nnode 3: [4,5]\nnode 4: [3,4]\nnode 5: [2,3]\nnode 6: [2,3]\nnode 7: [2,3]\nnode 8: [7,6]\nnode 9: [1,1]\nnode 10: [2,3]." - } - ] - }, - { - "id": "gnn-hard-graph624", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [0,0]\nnode 10: [0,1]\nnode 11: [0,1]\nnode 12: [0,0]\nnode 13: [1,0]\nThe edges are: (0,7) (1,6) (10,1) (11,1) (6,2) (3,7) (4,3) (11,3) (4,12) (4,8) (11,4) (13,5) (7,12) (7,10) (8,10) (9,11) (10,12) (13,11) (13,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [5,4]\nnode 2: [1,2]\nnode 3: [5,3]\nnode 4: [9,4]\nnode 5: [0,1]\nnode 6: [2,2]\nnode 7: [7,3]\nnode 8: [2,2]\nnode 9: [3,1]\nnode 10: [6,5]\nnode 11: [4,6]\nnode 12: [3,4]\nnode 13: [7,2]." - } - ] - }, - { - "id": "gnn-hard-graph429", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [0,1]\nnode 10: [1,0]\nnode 11: [0,0]\nThe edges are: (0,2) (1,4) (6,1) (5,2) (2,6) (6,3) (4,9) (11,5) (6,5) (7,6) (6,8) (7,11) (10,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,3]\nnode 1: [4,7]\nnode 2: [4,6]\nnode 3: [3,5]\nnode 4: [1,3]\nnode 5: [6,10]\nnode 6: [8,9]\nnode 7: [5,8]\nnode 8: [3,5]\nnode 9: [1,2]\nnode 10: [2,1]\nnode 11: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph46", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [0,0]\nnode 8: [0,0]\nThe edges are: (7,0) (0,4) (0,2) (0,8) (1,6) (3,1) (1,5) (2,1) (1,8) (2,7) (2,4) (6,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,5]\nnode 1: [2,5]\nnode 2: [10,6]\nnode 3: [4,2]\nnode 4: [2,3]\nnode 5: [4,2]\nnode 6: [7,4]\nnode 7: [2,2]\nnode 8: [5,3]." - } - ] - }, - { - "id": "gnn-hard-graph425", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [0,1]\nnode 11: [1,1]\nThe edges are: (0,11) (11,1) (2,1) (2,5) (11,3) (3,5) (7,3) (10,3) (7,4) (8,5) (11,6) (7,9) (7,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [2,3]\nnode 2: [3,1]\nnode 3: [3,5]\nnode 4: [0,3]\nnode 5: [5,5]\nnode 6: [1,2]\nnode 7: [6,3]\nnode 8: [1,0]\nnode 9: [0,3]\nnode 10: [3,6]\nnode 11: [7,6]." - } - ] - }, - { - "id": "gnn-hard-graph12", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [0,1]\nThe edges are: (0,1) (4,1) (1,8) (2,6) (6,3) (6,4) (4,7) (5,7) (7,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [2,5]\nnode 2: [3,2]\nnode 3: [3,2]\nnode 4: [5,4]\nnode 5: [1,1]\nnode 6: [5,6]\nnode 7: [6,6]\nnode 8: [1,1]." - } - ] - }, - { - "id": "gnn-hard-graph139", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [1,1]\nThe edges are: (2,0) (0,6) (1,9) (1,4) (3,9) (4,8) (6,5) (5,8) (9,5) (9,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,0]\nnode 1: [2,4]\nnode 2: [2,1]\nnode 3: [1,3]\nnode 4: [1,1]\nnode 5: [2,3]\nnode 6: [5,3]\nnode 7: [1,3]\nnode 8: [4,3]\nnode 9: [6,5]." - } - ] - }, - { - "id": "gnn-hard-graph344", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [1,1]\nnode 9: [1,0]\nnode 10: [0,0]\nThe edges are: (10,0) (9,0) (7,0) (3,1) (10,1) (1,9) (5,2) (6,2) (3,6) (7,3) (4,10) (4,9) (8,5) (7,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,2]\nnode 1: [5,4]\nnode 2: [2,2]\nnode 3: [6,1]\nnode 4: [4,2]\nnode 5: [1,0]\nnode 6: [5,2]\nnode 7: [3,4]\nnode 8: [1,1]\nnode 9: [4,1]\nnode 10: [4,1]." - } - ] - }, - { - "id": "gnn-hard-graph745", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [1,0]\nnode 11: [0,1]\nnode 12: [1,1]\nnode 13: [1,0]\nnode 14: [0,0]\nThe edges are: (0,6) (0,8) (1,14) (5,1) (1,8) (2,6) (2,14) (13,2) (8,2) (2,7) (2,3) (9,3) (5,3) (13,3) (6,4) (5,6) (8,5) (9,6) (6,7) (8,10) (8,13) (11,14) (11,13) (13,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,4]\nnode 1: [7,4]\nnode 2: [11,13]\nnode 3: [7,7]\nnode 4: [3,3]\nnode 5: [8,6]\nnode 6: [9,8]\nnode 7: [6,5]\nnode 8: [7,7]\nnode 9: [4,5]\nnode 10: [4,1]\nnode 11: [2,5]\nnode 12: [1,3]\nnode 13: [10,5]\nnode 14: [4,2]." - } - ] - }, - { - "id": "gnn-hard-graph436", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [1,0]\nnode 9: [0,0]\nnode 10: [0,0]\nnode 11: [1,0]\nThe edges are: (9,0) (11,1) (7,1) (8,2) (6,3) (3,10) (4,7) (5,6) (11,5) (6,8) (6,7) (7,8) (7,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [5,2]\nnode 2: [2,1]\nnode 3: [2,3]\nnode 4: [4,1]\nnode 5: [3,3]\nnode 6: [9,4]\nnode 7: [9,4]\nnode 8: [7,3]\nnode 9: [4,1]\nnode 10: [1,1]\nnode 11: [4,1]." - } - ] - }, - { - "id": "gnn-hard-graph134", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [1,1]\nnode 9: [1,0]\nThe edges are: (3,0) (1,6) (1,5) (1,3) (2,7) (3,2) (8,2) (3,6) (5,4) (7,5) (8,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,2]\nnode 1: [6,4]\nnode 2: [7,4]\nnode 3: [3,6]\nnode 4: [1,1]\nnode 5: [2,2]\nnode 6: [5,3]\nnode 7: [2,4]\nnode 8: [2,4]\nnode 9: [2,1]." - } - ] - }, - { - "id": "gnn-hard-graph809", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,1]\nnode 10: [0,0]\nnode 11: [0,1]\nnode 12: [1,0]\nnode 13: [0,1]\nnode 14: [0,1]\nThe edges are: (7,0) (10,0) (0,5) (0,1) (9,1) (13,1) (1,10) (14,1) (4,1) (2,9) (2,7) (2,13) (3,6) (10,3) (3,5) (12,3) (6,4) (4,10) (10,5) (8,5) (13,6) (6,11) (10,6) (12,8) (11,9) (11,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,11]\nnode 1: [0,6]\nnode 2: [0,5]\nnode 3: [0,11]\nnode 4: [0,9]\nnode 5: [2,3]\nnode 6: [2,4]\nnode 7: [0,4]\nnode 8: [0,6]\nnode 9: [1,8]\nnode 10: [1,11]\nnode 11: [0,8]\nnode 12: [3,1]\nnode 13: [0,10]\nnode 14: [0,4]." - } - ] - }, - { - "id": "gnn-hard-graph679", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [1,0]\nnode 11: [1,1]\nnode 12: [0,0]\nnode 13: [1,1]\nThe edges are: (0,8) (6,0) (0,4) (0,7) (10,1) (1,13) (7,1) (2,9) (2,3) (11,2) (2,7) (3,12) (3,10) (3,5) (3,7) (4,6) (4,11) (9,5) (7,9) (8,7) (10,7) (11,7) (13,9) (12,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,9]\nnode 1: [6,5]\nnode 2: [10,9]\nnode 3: [8,8]\nnode 4: [2,5]\nnode 5: [6,3]\nnode 6: [2,3]\nnode 7: [16,10]\nnode 8: [4,5]\nnode 9: [6,8]\nnode 10: [9,6]\nnode 11: [6,8]\nnode 12: [4,2]\nnode 13: [7,4]." - } - ] - }, - { - "id": "gnn-hard-graph75", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [1,0]\nThe edges are: (5,0) (0,2) (7,0) (6,1) (1,8) (2,1) (2,6) (6,3) (8,4) (7,4) (5,7) (8,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,1]\nnode 1: [7,2]\nnode 2: [6,1]\nnode 3: [3,1]\nnode 4: [5,2]\nnode 5: [5,1]\nnode 6: [5,1]\nnode 7: [6,0]\nnode 8: [6,1]." - } - ] - }, - { - "id": "gnn-hard-graph776", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,0]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [0,0]\nnode 11: [0,0]\nnode 12: [0,1]\nnode 13: [1,1]\nnode 14: [0,1]\nThe edges are: (12,0) (0,9) (13,0) (3,0) (1,6) (10,1) (12,1) (9,1) (9,2) (3,2) (3,14) (9,4) (14,4) (9,5) (6,12) (6,8) (8,7) (14,7) (8,10) (9,8) (9,11) (11,10) (14,11) (12,13) (13,14)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [11,9]\nnode 1: [10,5]\nnode 2: [6,4]\nnode 3: [3,6]\nnode 4: [6,4]\nnode 5: [4,2]\nnode 6: [6,5]\nnode 7: [3,3]\nnode 8: [6,4]\nnode 9: [3,12]\nnode 10: [2,5]\nnode 11: [7,4]\nnode 12: [4,9]\nnode 13: [7,7]\nnode 14: [3,10]." - } - ] - }, - { - "id": "gnn-hard-graph544", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [1,1]\nnode 10: [0,0]\nnode 11: [1,0]\nnode 12: [0,1]\nThe edges are: (9,0) (0,12) (2,0) (1,0) (1,10) (5,1) (12,1) (11,1) (4,2) (2,12) (4,3) (3,6) (8,5) (5,9) (6,11) (9,7) (9,12) (10,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,13]\nnode 1: [5,10]\nnode 2: [4,6]\nnode 3: [3,0]\nnode 4: [1,4]\nnode 5: [4,8]\nnode 6: [0,2]\nnode 7: [2,4]\nnode 8: [1,2]\nnode 9: [5,9]\nnode 10: [2,4]\nnode 11: [5,4]\nnode 12: [6,13]." - } - ] - }, - { - "id": "gnn-hard-graph320", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [1,1]\nThe edges are: (0,8) (1,10) (2,1) (4,3) (9,4) (8,4) (10,4) (5,10) (5,6) (5,7) (10,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,2]\nnode 1: [0,4]\nnode 2: [2,1]\nnode 3: [2,3]\nnode 4: [0,7]\nnode 5: [1,4]\nnode 6: [2,3]\nnode 7: [2,6]\nnode 8: [2,4]\nnode 9: [2,3]\nnode 10: [7,8]." - } - ] - }, - { - "id": "gnn-hard-graph17", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [0,1]\nThe edges are: (5,0) (0,6) (1,5) (2,1) (2,7) (2,3) (5,2) (4,2) (3,8) (7,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,4]\nnode 1: [6,6]\nnode 2: [9,10]\nnode 3: [3,4]\nnode 4: [3,3]\nnode 5: [9,8]\nnode 6: [2,1]\nnode 7: [6,6]\nnode 8: [1,2]." - } - ] - }, - { - "id": "gnn-hard-graph655", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [0,1]\nnode 10: [0,1]\nnode 11: [1,0]\nnode 12: [0,0]\nnode 13: [1,1]\nThe edges are: (6,0) (0,2) (13,0) (0,8) (10,0) (9,0) (7,0) (8,1) (4,1) (7,1) (11,2) (2,10) (2,3) (5,3) (8,3) (3,12) (3,4) (4,11) (13,4) (7,4) (5,11) (5,12) (6,11) (10,6) (12,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,14]\nnode 1: [4,7]\nnode 2: [10,14]\nnode 3: [7,12]\nnode 4: [10,13]\nnode 5: [8,9]\nnode 6: [7,11]\nnode 7: [10,15]\nnode 8: [8,12]\nnode 9: [3,6]\nnode 10: [5,11]\nnode 11: [6,9]\nnode 12: [5,6]\nnode 13: [6,9]." - } - ] - }, - { - "id": "gnn-hard-graph314", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [0,0]\nnode 10: [0,0]\nThe edges are: (3,0) (2,0) (10,1) (4,1) (1,9) (2,7) (6,2) (7,3) (3,10) (8,4) (5,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,0]\nnode 1: [5,5]\nnode 2: [5,3]\nnode 3: [6,4]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [1,0]\nnode 7: [2,0]\nnode 8: [2,2]\nnode 9: [0,0]\nnode 10: [1,0]." - } - ] - }, - { - "id": "gnn-hard-graph113", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [1,0]\nThe edges are: (0,2) (0,1) (1,8) (6,2) (8,3) (6,3) (4,8) (6,4) (8,5) (6,8) (8,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,3]\nnode 1: [6,5]\nnode 2: [6,1]\nnode 3: [8,4]\nnode 4: [8,4]\nnode 5: [4,4]\nnode 6: [6,8]\nnode 7: [4,4]\nnode 8: [9,3]." - } - ] - }, - { - "id": "gnn-hard-graph438", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [0,0]\nnode 11: [0,0]\nThe edges are: (9,0) (0,8) (4,0) (0,11) (10,0) (1,6) (1,11) (6,2) (3,2) (10,3) (4,8) (4,7) (4,11) (5,9) (8,6) (10,6) (11,9) (10,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [9,10]\nnode 1: [6,5]\nnode 2: [3,2]\nnode 3: [1,3]\nnode 4: [9,6]\nnode 5: [1,1]\nnode 6: [3,4]\nnode 7: [1,3]\nnode 8: [5,7]\nnode 9: [7,6]\nnode 10: [9,7]\nnode 11: [5,8]." - } - ] - }, - { - "id": "gnn-hard-graph734", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [0,0]\nnode 10: [0,0]\nnode 11: [1,1]\nnode 12: [1,0]\nnode 13: [1,0]\nnode 14: [1,0]\nThe edges are: (0,12) (3,0) (0,14) (7,0) (11,0) (1,0) (1,12) (10,1) (1,7) (4,1) (6,1) (10,2) (14,2) (2,7) (8,2) (14,3) (3,7) (3,5) (4,7) (4,6) (5,9) (13,5) (11,5) (6,8) (7,8) (10,8) (9,13) (10,9) (12,10) (13,11) (11,14) (13,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [22,18]\nnode 1: [19,12]\nnode 2: [10,12]\nnode 3: [16,13]\nnode 4: [10,9]\nnode 5: [13,8]\nnode 6: [7,9]\nnode 7: [19,16]\nnode 8: [10,7]\nnode 9: [8,5]\nnode 10: [12,10]\nnode 11: [15,11]\nnode 12: [15,10]\nnode 13: [12,6]\nnode 14: [16,9]." - } - ] - }, - { - "id": "gnn-hard-graph639", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [0,0]\nnode 9: [0,0]\nnode 10: [0,0]\nnode 11: [0,1]\nnode 12: [0,1]\nnode 13: [1,1]\nThe edges are: (0,1) (5,0) (0,10) (11,0) (1,12) (1,13) (9,2) (3,4) (9,3) (4,8) (10,5) (5,11) (13,6) (7,12) (13,8) (9,13) (12,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,4]\nnode 1: [0,4]\nnode 2: [2,2]\nnode 3: [2,3]\nnode 4: [3,1]\nnode 5: [0,2]\nnode 6: [0,1]\nnode 7: [0,2]\nnode 8: [0,2]\nnode 9: [1,1]\nnode 10: [0,2]\nnode 11: [0,4]\nnode 12: [1,4]\nnode 13: [6,6]." - } - ] - }, - { - "id": "gnn-hard-graph451", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [0,1]\nnode 11: [0,1]\nThe edges are: (0,8) (1,4) (10,2) (3,4) (5,3) (3,7) (3,11) (8,4) (4,9) (6,5) (7,5) (5,9) (8,6) (9,6) (10,7) (10,9) (11,9) (11,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [1,2]\nnode 2: [1,2]\nnode 3: [2,9]\nnode 4: [6,8]\nnode 5: [6,11]\nnode 6: [3,8]\nnode 7: [3,6]\nnode 8: [2,5]\nnode 9: [3,10]\nnode 10: [3,10]\nnode 11: [5,8]." - } - ] - }, - { - "id": "gnn-hard-graph388", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [0,0]\nnode 11: [1,1]\nThe edges are: (0,1) (7,0) (5,1) (8,1) (7,1) (2,4) (6,3) (10,4) (9,4) (5,8) (6,8) (7,11) (9,8) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [6,2]\nnode 1: [8,3]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [3,4]\nnode 5: [5,2]\nnode 6: [2,2]\nnode 7: [6,1]\nnode 8: [6,5]\nnode 9: [4,2]\nnode 10: [2,2]\nnode 11: [3,1]." - } - ] - }, - { - "id": "gnn-hard-graph137", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [0,0]\nnode 9: [1,0]\nThe edges are: (9,0) (8,0) (1,7) (5,1) (1,2) (1,4) (7,2) (8,2) (5,3) (4,6) (6,5) (7,6) (6,9) (8,7) (8,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,2]\nnode 1: [0,9]\nnode 2: [2,6]\nnode 3: [0,3]\nnode 4: [1,3]\nnode 5: [1,3]\nnode 6: [1,9]\nnode 7: [3,5]\nnode 8: [2,5]\nnode 9: [4,2]." - } - ] - }, - { - "id": "gnn-hard-graph589", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [0,1]\nnode 10: [0,1]\nnode 11: [1,0]\nnode 12: [1,1]\nThe edges are: (0,11) (1,2) (1,7) (12,1) (4,3) (10,3) (4,11) (10,4) (9,5) (12,5) (6,9) (12,6) (8,11) (12,8) (10,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [3,1]\nnode 2: [2,2]\nnode 3: [3,2]\nnode 4: [5,5]\nnode 5: [5,2]\nnode 6: [5,2]\nnode 7: [2,2]\nnode 8: [5,3]\nnode 9: [2,4]\nnode 10: [4,5]\nnode 11: [6,3]\nnode 12: [6,7]." - } - ] - }, - { - "id": "gnn-hard-graph415", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [0,0]\nnode 10: [0,1]\nnode 11: [1,1]\nThe edges are: (3,0) (0,11) (1,9) (1,7) (6,1) (2,4) (2,6) (3,10) (6,3) (8,5) (7,6) (7,8) (11,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [4,6]\nnode 2: [2,5]\nnode 3: [6,8]\nnode 4: [1,0]\nnode 5: [1,2]\nnode 6: [6,3]\nnode 7: [5,7]\nnode 8: [3,1]\nnode 9: [2,1]\nnode 10: [1,2]\nnode 11: [4,4]." - } - ] - }, - { - "id": "gnn-hard-graph607", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [1,0]\nnode 9: [0,1]\nnode 10: [0,0]\nnode 11: [1,0]\nnode 12: [1,0]\nnode 13: [1,1]\nThe edges are: (0,7) (0,9) (6,0) (0,3) (8,1) (6,1) (1,12) (5,1) (1,13) (1,10) (2,7) (2,9) (2,6) (9,3) (11,3) (4,11) (5,6) (6,11) (7,8) (9,8) (8,13) (9,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [14,6]\nnode 1: [12,10]\nnode 2: [12,5]\nnode 3: [9,7]\nnode 4: [2,2]\nnode 5: [8,3]\nnode 6: [11,9]\nnode 7: [5,9]\nnode 8: [14,5]\nnode 9: [9,12]\nnode 10: [4,1]\nnode 11: [12,5]\nnode 12: [4,1]\nnode 13: [6,5]." - } - ] - }, - { - "id": "gnn-hard-graph827", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [0,0]\nnode 10: [1,1]\nnode 11: [0,0]\nnode 12: [0,1]\nnode 13: [1,1]\nnode 14: [1,0]\nThe edges are: (11,0) (0,10) (0,14) (8,0) (2,0) (10,1) (2,7) (10,2) (3,14) (4,14) (4,6) (14,5) (5,12) (13,5) (10,6) (7,14) (12,7) (11,8) (13,8) (9,11) (10,9) (9,14) (10,12) (13,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,8]\nnode 1: [1,1]\nnode 2: [7,4]\nnode 3: [1,2]\nnode 4: [2,3]\nnode 5: [4,5]\nnode 6: [2,1]\nnode 7: [5,6]\nnode 8: [7,5]\nnode 9: [4,5]\nnode 10: [12,9]\nnode 11: [8,5]\nnode 12: [5,4]\nnode 13: [5,5]\nnode 14: [12,6]." - } - ] - }, - { - "id": "gnn-hard-graph91", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [0,0]\nThe edges are: (5,0) (0,8) (4,1) (5,2) (2,7) (3,6) (4,5) (8,4) (6,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,2]\nnode 1: [1,2]\nnode 2: [4,2]\nnode 3: [2,0]\nnode 4: [6,3]\nnode 5: [4,4]\nnode 6: [1,2]\nnode 7: [4,1]\nnode 8: [2,3]." - } - ] - }, - { - "id": "gnn-hard-graph194", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [0,1]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [1,1]\nThe edges are: (0,9) (2,0) (0,7) (9,1) (1,6) (3,2) (3,5) (4,7) (8,5) (7,9) (7,8) (9,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [6,8]\nnode 1: [2,4]\nnode 2: [2,5]\nnode 3: [3,3]\nnode 4: [3,3]\nnode 5: [2,5]\nnode 6: [1,2]\nnode 7: [7,10]\nnode 8: [7,7]\nnode 9: [8,11]." - } - ] - }, - { - "id": "gnn-hard-graph80", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,1]\nThe edges are: (0,5) (8,0) (0,3) (4,0) (7,1) (5,1) (6,1) (3,1) (4,1) (8,2) (2,4) (3,5) (8,6) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,10]\nnode 1: [6,8]\nnode 2: [4,6]\nnode 3: [7,11]\nnode 4: [6,11]\nnode 5: [6,11]\nnode 6: [6,9]\nnode 7: [6,9]\nnode 8: [5,8]." - } - ] - }, - { - "id": "gnn-hard-graph571", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [1,1]\nnode 9: [0,0]\nnode 10: [0,0]\nnode 11: [1,0]\nnode 12: [1,1]\nThe edges are: (0,3) (9,0) (0,4) (12,0) (1,5) (4,1) (1,6) (2,10) (2,11) (3,4) (4,11) (7,4) (9,5) (5,10) (11,6) (8,10) (12,9) (11,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,4]\nnode 1: [4,2]\nnode 2: [5,3]\nnode 3: [5,4]\nnode 4: [6,5]\nnode 5: [6,6]\nnode 6: [3,3]\nnode 7: [3,2]\nnode 8: [3,2]\nnode 9: [3,2]\nnode 10: [3,1]\nnode 11: [8,4]\nnode 12: [4,4]." - } - ] - }, - { - "id": "gnn-hard-graph312", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [0,0]\nnode 10: [0,0]\nThe edges are: (0,6) (0,3) (5,1) (6,1) (1,3) (2,3) (2,7) (3,5) (10,3) (4,8) (5,10) (9,5) (6,5) (9,7) (8,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [6,4]\nnode 4: [1,0]\nnode 5: [3,2]\nnode 6: [3,3]\nnode 7: [3,2]\nnode 8: [1,0]\nnode 9: [1,1]\nnode 10: [2,1]." - } - ] - }, - { - "id": "gnn-hard-graph164", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [0,0]\nThe edges are: (0,1) (2,0) (8,0) (3,1) (9,3) (4,3) (4,7) (5,7) (5,6) (6,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,0]\nnode 1: [2,1]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [4,1]\nnode 5: [5,2]\nnode 6: [5,3]\nnode 7: [5,4]\nnode 8: [1,1]\nnode 9: [1,0]." - } - ] - }, - { - "id": "gnn-hard-graph144", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [0,0]\nThe edges are: (7,0) (2,0) (3,1) (2,8) (2,3) (4,7) (9,4) (5,9) (9,6) (9,7) (8,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,3]\nnode 1: [2,1]\nnode 2: [5,4]\nnode 3: [4,2]\nnode 4: [3,4]\nnode 5: [2,3]\nnode 6: [2,3]\nnode 7: [5,6]\nnode 8: [5,5]\nnode 9: [3,3]." - } - ] - }, - { - "id": "gnn-hard-graph33", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [0,0]\nThe edges are: (0,5) (0,4) (3,0) (0,2) (0,6) (1,6) (6,2) (6,3) (3,8) (4,7) (5,7) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [9,8]\nnode 1: [1,2]\nnode 2: [3,4]\nnode 3: [4,6]\nnode 4: [3,3]\nnode 5: [3,3]\nnode 6: [7,4]\nnode 7: [5,6]\nnode 8: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph661", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [1,0]\nnode 11: [0,1]\nnode 12: [0,0]\nnode 13: [1,0]\nThe edges are: (0,1) (8,0) (1,9) (2,8) (11,2) (7,3) (10,3) (4,7) (8,4) (11,5) (12,5) (5,10) (13,6) (8,9) (11,9) (9,10) (10,11) (12,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,3]\nnode 1: [3,3]\nnode 2: [2,4]\nnode 3: [1,4]\nnode 4: [0,3]\nnode 5: [5,6]\nnode 6: [0,1]\nnode 7: [1,3]\nnode 8: [3,7]\nnode 9: [3,8]\nnode 10: [6,6]\nnode 11: [4,8]\nnode 12: [1,2]\nnode 13: [3,1]." - } - ] - }, - { - "id": "gnn-hard-graph783", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [1,0]\nnode 9: [1,0]\nnode 10: [1,0]\nnode 11: [0,1]\nnode 12: [1,0]\nnode 13: [0,1]\nnode 14: [1,0]\nThe edges are: (2,0) (6,1) (2,1) (8,2) (9,2) (5,2) (14,3) (12,3) (9,3) (4,3) (4,12) (4,13) (5,14) (5,7) (6,8) (11,7) (10,7) (8,11) (9,13) (10,13) (13,14)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,2]\nnode 1: [5,2]\nnode 2: [7,10]\nnode 3: [7,6]\nnode 4: [7,3]\nnode 5: [8,6]\nnode 6: [2,5]\nnode 7: [3,5]\nnode 8: [6,3]\nnode 9: [10,4]\nnode 10: [5,3]\nnode 11: [3,5]\nnode 12: [5,2]\nnode 13: [6,7]\nnode 14: [8,4]." - } - ] - }, - { - "id": "gnn-hard-graph313", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,0]\nnode 7: [0,0]\nnode 8: [0,0]\nnode 9: [1,1]\nnode 10: [0,0]\nThe edges are: (4,0) (0,1) (9,1) (3,1) (6,2) (5,3) (4,8) (5,6) (6,7) (10,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,1]\nnode 1: [4,4]\nnode 2: [0,1]\nnode 3: [3,1]\nnode 4: [3,1]\nnode 5: [1,3]\nnode 6: [3,0]\nnode 7: [0,1]\nnode 8: [1,0]\nnode 9: [2,1]\nnode 10: [1,0]." - } - ] - }, - { - "id": "gnn-hard-graph828", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [0,1]\nnode 11: [0,1]\nnode 12: [0,1]\nnode 13: [0,0]\nnode 14: [1,0]\nThe edges are: (0,12) (6,0) (11,0) (0,1) (1,14) (7,1) (1,13) (1,2) (9,1) (13,2) (2,9) (3,5) (4,13) (8,4) (10,4) (14,5) (8,5) (14,7) (8,7) (10,7) (10,8) (13,9) (11,12) (11,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,5]\nnode 1: [7,17]\nnode 2: [7,9]\nnode 3: [2,1]\nnode 4: [7,8]\nnode 5: [6,7]\nnode 6: [1,4]\nnode 7: [11,10]\nnode 8: [5,5]\nnode 9: [6,9]\nnode 10: [4,6]\nnode 11: [4,9]\nnode 12: [2,5]\nnode 13: [6,9]\nnode 14: [7,6]." - } - ] - }, - { - "id": "gnn-hard-graph567", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [0,1]\nnode 10: [0,0]\nnode 11: [1,1]\nnode 12: [0,1]\nThe edges are: (10,0) (0,11) (0,2) (5,1) (1,7) (10,1) (1,12) (8,2) (3,2) (2,12) (3,6) (7,3) (8,3) (4,7) (8,4) (4,9) (12,4) (5,6) (8,6) (6,10) (6,9) (7,8) (8,10) (9,8) (8,11) (12,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,9]\nnode 1: [8,8]\nnode 2: [8,12]\nnode 3: [7,15]\nnode 4: [9,13]\nnode 5: [3,4]\nnode 6: [8,11]\nnode 7: [7,11]\nnode 8: [10,22]\nnode 9: [5,11]\nnode 10: [7,11]\nnode 11: [7,10]\nnode 12: [5,11]." - } - ] - }, - { - "id": "gnn-hard-graph255", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [0,0]\nnode 9: [0,0]\nnode 10: [1,0]\nThe edges are: (9,0) (0,3) (0,8) (2,0) (1,6) (2,6) (2,8) (3,10) (3,9) (3,5) (4,10) (9,4) (4,5) (5,10) (6,8) (8,7) (9,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [9,10]\nnode 1: [1,1]\nnode 2: [5,6]\nnode 3: [4,6]\nnode 4: [3,5]\nnode 5: [6,5]\nnode 6: [6,7]\nnode 7: [3,4]\nnode 8: [5,6]\nnode 9: [9,8]\nnode 10: [6,4]." - } - ] - }, - { - "id": "gnn-hard-graph100", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [1,0]\nThe edges are: (6,0) (0,4) (7,0) (8,0) (7,1) (4,2) (8,2) (2,5) (3,4) (7,3) (7,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,5]\nnode 1: [0,2]\nnode 2: [4,3]\nnode 3: [1,3]\nnode 4: [4,6]\nnode 5: [1,3]\nnode 6: [2,3]\nnode 7: [6,7]\nnode 8: [3,4]." - } - ] - }, - { - "id": "gnn-hard-graph178", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [1,0]\nThe edges are: (3,0) (8,0) (0,1) (2,1) (5,1) (4,3) (3,5) (8,3) (7,4) (9,4) (5,6) (7,5) (9,7) (9,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,5]\nnode 1: [6,3]\nnode 2: [2,2]\nnode 3: [9,5]\nnode 4: [7,4]\nnode 5: [8,4]\nnode 6: [3,2]\nnode 7: [7,5]\nnode 8: [7,5]\nnode 9: [6,2]." - } - ] - }, - { - "id": "gnn-hard-graph359", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [0,0]\nThe edges are: (1,0) (10,0) (3,0) (4,1) (6,1) (1,3) (2,8) (5,3) (8,3) (4,8) (4,10) (8,5) (7,5) (9,7) (7,10) (8,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,5]\nnode 1: [5,5]\nnode 2: [0,3]\nnode 3: [3,6]\nnode 4: [3,6]\nnode 5: [2,7]\nnode 6: [1,1]\nnode 7: [4,4]\nnode 8: [5,5]\nnode 9: [0,5]\nnode 10: [2,4]." - } - ] - }, - { - "id": "gnn-hard-graph324", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [0,1]\nnode 10: [1,0]\nThe edges are: (0,8) (4,0) (0,9) (2,1) (1,9) (3,2) (8,3) (6,4) (4,7) (5,6) (8,6) (6,7) (10,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [6,2]\nnode 1: [4,0]\nnode 2: [0,4]\nnode 3: [5,1]\nnode 4: [0,7]\nnode 5: [0,2]\nnode 6: [4,5]\nnode 7: [1,3]\nnode 8: [0,8]\nnode 9: [0,5]\nnode 10: [3,1]." - } - ] - }, - { - "id": "gnn-hard-graph424", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [0,0]\nnode 11: [1,1]\nThe edges are: (0,4) (0,7) (1,6) (2,5) (2,4) (9,3) (11,3) (4,3) (8,3) (11,6) (6,8) (11,7) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,4]\nnode 1: [1,1]\nnode 2: [3,2]\nnode 3: [4,8]\nnode 4: [2,4]\nnode 5: [1,1]\nnode 6: [3,6]\nnode 7: [1,4]\nnode 8: [2,3]\nnode 9: [1,3]\nnode 10: [0,1]\nnode 11: [4,5]." - } - ] - }, - { - "id": "gnn-hard-graph264", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [0,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [1,1]\nnode 10: [0,1]\nThe edges are: (0,3) (2,0) (0,9) (5,1) (3,2) (2,10) (2,9) (10,3) (3,9) (3,8) (6,4) (9,4) (5,9) (8,5) (7,5) (9,6) (7,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [11,10]\nnode 1: [3,4]\nnode 2: [11,10]\nnode 3: [13,12]\nnode 4: [6,5]\nnode 5: [10,9]\nnode 6: [7,6]\nnode 7: [8,8]\nnode 8: [6,7]\nnode 9: [16,17]\nnode 10: [6,6]." - } - ] - }, - { - "id": "gnn-hard-graph173", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [1,0]\nThe edges are: (0,7) (4,0) (2,1) (4,1) (9,1) (3,5) (8,3) (9,4) (7,6) (6,8) (9,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,3]\nnode 1: [6,5]\nnode 2: [2,2]\nnode 3: [1,0]\nnode 4: [7,6]\nnode 5: [1,1]\nnode 6: [5,3]\nnode 7: [4,3]\nnode 8: [3,2]\nnode 9: [6,5]." - } - ] - }, - { - "id": "gnn-hard-graph576", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [1,1]\nnode 11: [0,0]\nnode 12: [1,0]\nThe edges are: (0,7) (6,0) (1,4) (1,7) (1,5) (1,12) (1,3) (6,1) (12,2) (2,9) (11,3) (3,6) (4,12) (10,4) (11,6) (6,12) (9,6) (9,8) (9,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,1]\nnode 1: [10,6]\nnode 2: [5,5]\nnode 3: [9,5]\nnode 4: [9,7]\nnode 5: [5,3]\nnode 6: [14,11]\nnode 7: [7,4]\nnode 8: [2,2]\nnode 9: [9,6]\nnode 10: [2,1]\nnode 11: [4,2]\nnode 12: [14,8]." - } - ] - }, - { - "id": "gnn-hard-graph182", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [1,0]\nThe edges are: (0,5) (2,1) (1,4) (1,7) (8,1) (1,3) (3,2) (3,4) (6,4) (8,5) (6,8) (6,9) (9,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [11,2]\nnode 2: [6,5]\nnode 3: [6,3]\nnode 4: [9,7]\nnode 5: [5,0]\nnode 6: [8,1]\nnode 7: [3,3]\nnode 8: [10,7]\nnode 9: [7,2]." - } - ] - }, - { - "id": "gnn-hard-graph157", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [0,0]\nnode 8: [0,0]\nnode 9: [0,1]\nThe edges are: (5,0) (0,3) (2,1) (8,1) (4,1) (6,2) (2,4) (3,9) (4,3) (6,7) (9,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,4]\nnode 1: [3,4]\nnode 2: [4,2]\nnode 3: [4,4]\nnode 4: [2,6]\nnode 5: [1,2]\nnode 6: [2,3]\nnode 7: [1,0]\nnode 8: [2,2]\nnode 9: [0,4]." - } - ] - }, - { - "id": "gnn-hard-graph782", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [1,1]\nnode 10: [1,0]\nnode 11: [1,0]\nnode 12: [0,0]\nnode 13: [0,0]\nnode 14: [0,1]\nThe edges are: (0,11) (0,12) (7,0) (1,13) (3,1) (1,2) (1,6) (3,2) (2,5) (3,12) (3,9) (3,7) (4,3) (4,13) (14,4) (9,5) (13,7) (7,8) (8,12) (8,9) (8,14) (9,13) (10,9) (12,13) (14,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,5]\nnode 1: [5,7]\nnode 2: [6,5]\nnode 3: [13,13]\nnode 4: [4,5]\nnode 5: [6,4]\nnode 6: [2,2]\nnode 7: [5,6]\nnode 8: [9,8]\nnode 9: [7,8]\nnode 10: [4,2]\nnode 11: [1,0]\nnode 12: [6,7]\nnode 13: [11,11]\nnode 14: [4,7]." - } - ] - }, - { - "id": "gnn-hard-graph116", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [0,1]\nThe edges are: (7,0) (7,1) (4,1) (6,1) (2,1) (2,3) (4,2) (5,3) (4,6) (4,5) (5,7) (8,6) (8,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [11,6]\nnode 2: [9,7]\nnode 3: [5,3]\nnode 4: [10,9]\nnode 5: [8,4]\nnode 6: [8,8]\nnode 7: [6,9]\nnode 8: [4,3]." - } - ] - }, - { - "id": "gnn-hard-graph404", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [0,0]\nnode 10: [1,1]\nnode 11: [1,0]\nThe edges are: (3,0) (5,0) (10,1) (1,3) (1,9) (1,2) (5,1) (2,3) (5,2) (3,9) (3,8) (7,3) (10,4) (4,9) (11,4) (5,11) (5,6) (11,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [6,4]\nnode 1: [12,6]\nnode 2: [9,7]\nnode 3: [12,8]\nnode 4: [5,1]\nnode 5: [12,5]\nnode 6: [5,1]\nnode 7: [3,3]\nnode 8: [3,3]\nnode 9: [8,7]\nnode 10: [5,4]\nnode 11: [7,2]." - } - ] - }, - { - "id": "gnn-hard-graph834", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [1,0]\nnode 10: [0,1]\nnode 11: [0,0]\nnode 12: [0,0]\nnode 13: [1,1]\nnode 14: [0,1]\nThe edges are: (0,4) (1,3) (1,12) (10,1) (1,9) (7,2) (2,8) (3,13) (3,8) (4,14) (4,9) (5,4) (8,4) (9,5) (12,6) (6,7) (7,10) (8,12) (9,8) (14,11) (12,14)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [4,11]\nnode 2: [5,2]\nnode 3: [7,1]\nnode 4: [10,2]\nnode 5: [4,4]\nnode 6: [1,6]\nnode 7: [3,5]\nnode 8: [6,13]\nnode 9: [10,3]\nnode 10: [3,3]\nnode 11: [1,0]\nnode 12: [8,2]\nnode 13: [1,3]\nnode 14: [2,7]." - } - ] - }, - { - "id": "gnn-hard-graph657", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [0,0]\nnode 10: [1,0]\nnode 11: [0,0]\nnode 12: [1,1]\nnode 13: [1,0]\nThe edges are: (2,0) (12,1) (7,1) (2,9) (2,4) (13,3) (4,3) (10,3) (5,4) (12,4) (11,4) (5,9) (5,12) (7,5) (6,9) (6,12) (7,10) (9,8) (12,9) (11,9) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,0]\nnode 1: [6,0]\nnode 2: [9,6]\nnode 3: [4,5]\nnode 4: [8,1]\nnode 5: [14,5]\nnode 6: [8,2]\nnode 7: [5,3]\nnode 8: [5,2]\nnode 9: [8,3]\nnode 10: [10,2]\nnode 11: [8,5]\nnode 12: [13,8]\nnode 13: [2,0]." - } - ] - }, - { - "id": "gnn-hard-graph483", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [1,0]\nnode 10: [0,0]\nnode 11: [0,0]\nnode 12: [0,1]\nThe edges are: (0,11) (0,5) (7,0) (4,0) (4,1) (6,1) (1,9) (10,2) (5,2) (2,7) (3,8) (4,5) (4,9) (11,5) (5,9) (10,6) (6,9) (7,10) (9,8) (12,8) (12,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,3]\nnode 1: [5,4]\nnode 2: [3,6]\nnode 3: [1,2]\nnode 4: [9,5]\nnode 5: [10,5]\nnode 6: [5,7]\nnode 7: [6,6]\nnode 8: [2,2]\nnode 9: [8,6]\nnode 10: [3,3]\nnode 11: [5,2]\nnode 12: [2,6]." - } - ] - }, - { - "id": "gnn-hard-graph543", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [1,0]\nnode 9: [0,1]\nnode 10: [0,0]\nnode 11: [0,0]\nnode 12: [0,1]\nThe edges are: (0,9) (0,7) (0,8) (6,0) (9,1) (10,1) (8,1) (4,2) (9,2) (2,5) (12,2) (8,3) (10,4) (11,4) (6,4) (5,11) (10,7) (7,8) (8,9) (8,12) (10,9) (11,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [10,7]\nnode 1: [8,10]\nnode 2: [9,2]\nnode 3: [3,5]\nnode 4: [4,12]\nnode 5: [2,7]\nnode 6: [4,4]\nnode 7: [6,12]\nnode 8: [12,5]\nnode 9: [8,17]\nnode 10: [9,3]\nnode 11: [5,1]\nnode 12: [5,12]." - } - ] - }, - { - "id": "gnn-hard-graph733", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [0,0]\nnode 9: [1,1]\nnode 10: [1,0]\nnode 11: [1,1]\nnode 12: [0,0]\nnode 13: [1,0]\nnode 14: [0,1]\nThe edges are: (0,13) (0,2) (1,10) (12,1) (1,4) (5,2) (3,10) (3,7) (3,14) (4,8) (6,7) (14,6) (7,12) (11,8) (10,9) (9,11) (14,9) (10,13) (14,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,2]\nnode 1: [3,2]\nnode 2: [3,0]\nnode 3: [7,5]\nnode 4: [2,1]\nnode 5: [1,1]\nnode 6: [4,3]\nnode 7: [1,2]\nnode 8: [1,1]\nnode 9: [7,5]\nnode 10: [6,4]\nnode 11: [3,3]\nnode 12: [2,1]\nnode 13: [8,4]\nnode 14: [5,5]." - } - ] - }, - { - "id": "gnn-hard-graph37", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [0,0]\nThe edges are: (7,0) (8,1) (3,1) (2,7) (3,7) (3,5) (3,6) (5,4) (4,8) (6,7) (6,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,3]\nnode 1: [5,5]\nnode 2: [1,3]\nnode 3: [3,4]\nnode 4: [3,2]\nnode 5: [4,3]\nnode 6: [6,8]\nnode 7: [6,6]\nnode 8: [2,1]." - } - ] - }, - { - "id": "gnn-hard-graph334", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [1,0]\nnode 10: [0,1]\nThe edges are: (5,0) (6,1) (1,4) (1,2) (5,2) (3,5) (7,4) (5,9) (10,8) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [5,4]\nnode 2: [4,4]\nnode 3: [2,2]\nnode 4: [2,3]\nnode 5: [5,2]\nnode 6: [2,2]\nnode 7: [2,2]\nnode 8: [2,1]\nnode 9: [4,3]\nnode 10: [1,2]." - } - ] - }, - { - "id": "gnn-hard-graph285", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [0,0]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [1,1]\nThe edges are: (8,0) (4,0) (0,3) (6,0) (2,1) (1,5) (2,8) (7,3) (3,6) (4,10) (5,8) (5,10) (9,6) (10,6) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,5]\nnode 1: [1,3]\nnode 2: [3,2]\nnode 3: [3,7]\nnode 4: [2,6]\nnode 5: [4,4]\nnode 6: [5,9]\nnode 7: [2,1]\nnode 8: [2,7]\nnode 9: [3,4]\nnode 10: [6,7]." - } - ] - }, - { - "id": "gnn-hard-graph803", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [0,1]\nnode 11: [1,0]\nnode 12: [1,0]\nnode 13: [1,0]\nnode 14: [1,1]\nThe edges are: (0,3) (6,0) (2,1) (14,1) (10,1) (9,2) (8,2) (3,2) (2,10) (3,4) (9,3) (3,12) (4,13) (4,9) (6,4) (5,10) (6,5) (12,5) (8,6) (7,14) (11,7) (10,7) (8,10) (12,8) (10,13) (12,10) (13,11) (12,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,5]\nnode 1: [5,6]\nnode 2: [12,13]\nnode 3: [13,13]\nnode 4: [11,10]\nnode 5: [9,7]\nnode 6: [10,6]\nnode 7: [5,2]\nnode 8: [11,11]\nnode 9: [10,9]\nnode 10: [14,17]\nnode 11: [7,7]\nnode 12: [13,8]\nnode 13: [9,4]\nnode 14: [3,5]." - } - ] - }, - { - "id": "gnn-hard-graph237", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [1,0]\nThe edges are: (0,9) (1,0) (5,0) (8,1) (1,6) (5,1) (7,2) (3,4) (4,7) (4,8) (6,4) (5,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,2]\nnode 1: [4,2]\nnode 2: [1,1]\nnode 3: [2,2]\nnode 4: [2,2]\nnode 5: [6,4]\nnode 6: [6,4]\nnode 7: [2,2]\nnode 8: [5,4]\nnode 9: [2,1]." - } - ] - }, - { - "id": "gnn-hard-graph258", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [1,0]\nnode 9: [1,1]\nnode 10: [1,1]\nThe edges are: (7,0) (0,9) (1,4) (2,1) (5,1) (3,2) (2,7) (8,2) (2,10) (6,3) (9,3) (10,3) (7,4) (7,9) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,4]\nnode 1: [3,4]\nnode 2: [8,7]\nnode 3: [8,5]\nnode 4: [4,3]\nnode 5: [2,1]\nnode 6: [2,3]\nnode 7: [6,6]\nnode 8: [3,2]\nnode 9: [7,7]\nnode 10: [7,7]." - } - ] - }, - { - "id": "gnn-hard-graph556", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [0,0]\nnode 10: [1,1]\nnode 11: [1,0]\nnode 12: [1,0]\nThe edges are: (7,0) (9,0) (0,3) (0,11) (2,1) (1,9) (1,5) (6,1) (1,10) (2,6) (12,3) (3,10) (3,8) (4,7) (4,12) (4,10) (7,5) (5,12) (5,6) (11,5) (12,6) (7,12) (7,9) (7,10) (8,7) (9,11) (11,10) (11,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [12,9]\nnode 1: [11,4]\nnode 2: [5,2]\nnode 3: [5,5]\nnode 4: [8,6]\nnode 5: [14,9]\nnode 6: [8,6]\nnode 7: [12,8]\nnode 8: [7,6]\nnode 9: [10,8]\nnode 10: [14,11]\nnode 11: [10,6]\nnode 12: [18,10]." - } - ] - }, - { - "id": "gnn-hard-graph617", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [0,1]\nnode 12: [0,1]\nnode 13: [0,1]\nThe edges are: (0,3) (0,2) (0,5) (12,0) (11,1) (1,13) (12,1) (3,4) (5,3) (4,6) (9,5) (12,5) (6,7) (6,12) (7,12) (8,11) (8,10) (9,10) (11,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,10]\nnode 1: [5,6]\nnode 2: [1,3]\nnode 3: [2,8]\nnode 4: [2,4]\nnode 5: [8,10]\nnode 6: [3,5]\nnode 7: [3,5]\nnode 8: [1,4]\nnode 9: [1,6]\nnode 10: [3,4]\nnode 11: [2,6]\nnode 12: [2,13]\nnode 13: [1,5]." - } - ] - }, - { - "id": "gnn-hard-graph353", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [0,1]\nThe edges are: (0,1) (2,0) (0,10) (1,8) (2,7) (2,8) (2,6) (4,2) (3,8) (3,5) (3,9) (5,4) (6,5) (9,7) (8,9) (8,10) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,7]\nnode 1: [3,5]\nnode 2: [7,6]\nnode 3: [3,5]\nnode 4: [2,2]\nnode 5: [3,2]\nnode 6: [2,2]\nnode 7: [1,4]\nnode 8: [3,11]\nnode 9: [6,9]\nnode 10: [3,7]." - } - ] - }, - { - "id": "gnn-hard-graph706", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [1,0]\nnode 12: [0,0]\nnode 13: [0,1]\nThe edges are: (0,12) (5,0) (4,0) (1,4) (1,3) (2,12) (2,4) (2,13) (6,3) (11,3) (3,4) (3,7) (4,10) (5,4) (13,8) (10,9) (12,9) (10,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,8]\nnode 1: [9,8]\nnode 2: [9,6]\nnode 3: [6,10]\nnode 4: [7,13]\nnode 5: [6,5]\nnode 6: [4,4]\nnode 7: [4,4]\nnode 8: [2,0]\nnode 9: [3,4]\nnode 10: [7,7]\nnode 11: [5,6]\nnode 12: [2,4]\nnode 13: [0,3]." - } - ] - }, - { - "id": "gnn-hard-graph427", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [1,0]\nnode 10: [0,1]\nnode 11: [0,1]\nThe edges are: (0,8) (1,4) (11,2) (6,2) (3,4) (3,6) (5,4) (4,7) (10,4) (5,8) (6,5) (6,11) (6,9) (7,8) (8,11) (11,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [3,2]\nnode 2: [4,4]\nnode 3: [6,3]\nnode 4: [7,5]\nnode 5: [8,5]\nnode 6: [7,9]\nnode 7: [5,4]\nnode 8: [4,7]\nnode 9: [3,1]\nnode 10: [4,5]\nnode 11: [7,6]." - } - ] - }, - { - "id": "gnn-hard-graph729", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [0,0]\nnode 9: [1,0]\nnode 10: [0,0]\nnode 11: [1,0]\nnode 12: [1,0]\nnode 13: [1,0]\nnode 14: [0,1]\nThe edges are: (3,0) (5,0) (0,4) (0,14) (1,2) (1,7) (14,1) (1,11) (14,2) (4,3) (3,14) (8,4) (12,4) (4,7) (5,8) (13,6) (6,12) (10,6) (7,9) (8,10) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,5]\nnode 1: [2,6]\nnode 2: [3,4]\nnode 3: [3,7]\nnode 4: [4,6]\nnode 5: [2,4]\nnode 6: [4,0]\nnode 7: [3,5]\nnode 8: [3,2]\nnode 9: [3,1]\nnode 10: [3,2]\nnode 11: [2,2]\nnode 12: [3,2]\nnode 13: [2,0]\nnode 14: [3,8]." - } - ] - }, - { - "id": "gnn-hard-graph638", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [1,0]\nnode 10: [1,0]\nnode 11: [1,0]\nnode 12: [1,1]\nnode 13: [1,0]\nThe edges are: (0,12) (4,0) (7,0) (6,0) (7,1) (4,2) (3,11) (7,4) (4,8) (5,13) (5,6) (7,9) (13,8) (8,11) (12,9) (10,12) (13,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,1]\nnode 1: [2,0]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [10,2]\nnode 5: [1,2]\nnode 6: [6,3]\nnode 7: [8,3]\nnode 8: [3,1]\nnode 9: [4,0]\nnode 10: [2,0]\nnode 11: [5,1]\nnode 12: [7,4]\nnode 13: [6,1]." - } - ] - }, - { - "id": "gnn-hard-graph149", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [1,0]\nnode 9: [0,0]\nThe edges are: (1,0) (1,8) (1,4) (1,6) (8,2) (4,2) (2,9) (5,2) (3,8) (4,8) (4,5) (8,5) (7,5) (5,9) (7,9) (9,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,2]\nnode 1: [8,5]\nnode 2: [11,5]\nnode 3: [3,2]\nnode 4: [12,5]\nnode 5: [10,4]\nnode 6: [4,2]\nnode 7: [5,2]\nnode 8: [15,5]\nnode 9: [8,3]." - } - ] - }, - { - "id": "gnn-hard-graph725", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [0,0]\nnode 11: [0,0]\nnode 12: [1,0]\nnode 13: [0,0]\nnode 14: [1,1]\nThe edges are: (3,0) (0,4) (2,0) (0,1) (14,1) (2,3) (2,7) (11,2) (5,3) (4,3) (3,14) (11,3) (4,12) (9,5) (5,14) (5,13) (6,12) (10,7) (7,11) (10,8) (8,14) (14,9) (10,14)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,3]\nnode 1: [2,3]\nnode 2: [3,5]\nnode 3: [7,6]\nnode 4: [3,3]\nnode 5: [7,5]\nnode 6: [1,0]\nnode 7: [4,3]\nnode 8: [4,4]\nnode 9: [4,4]\nnode 10: [3,4]\nnode 11: [3,3]\nnode 12: [2,0]\nnode 13: [2,2]\nnode 14: [10,9]." - } - ] - }, - { - "id": "gnn-hard-graph480", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [1,0]\nnode 10: [0,0]\nnode 11: [0,1]\nnode 12: [0,0]\nThe edges are: (0,7) (3,1) (5,1) (1,7) (6,2) (3,12) (11,3) (3,10) (4,8) (6,12) (11,7) (7,10) (11,8) (12,9) (9,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,2]\nnode 1: [0,3]\nnode 2: [0,1]\nnode 3: [10,3]\nnode 4: [1,1]\nnode 5: [2,1]\nnode 6: [4,2]\nnode 7: [8,2]\nnode 8: [3,2]\nnode 9: [6,2]\nnode 10: [0,3]\nnode 11: [1,5]\nnode 12: [0,3]." - } - ] - }, - { - "id": "gnn-hard-graph126", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [1,0]\nThe edges are: (4,0) (2,0) (1,9) (1,4) (3,1) (1,2) (1,8) (5,2) (8,4) (9,5) (5,8) (6,5) (7,6) (8,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,5]\nnode 1: [3,9]\nnode 2: [5,5]\nnode 3: [2,2]\nnode 4: [4,5]\nnode 5: [3,5]\nnode 6: [2,4]\nnode 7: [2,2]\nnode 8: [5,9]\nnode 9: [4,4]." - } - ] - }, - { - "id": "gnn-hard-graph798", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [0,1]\nnode 11: [0,0]\nnode 12: [0,0]\nnode 13: [1,0]\nnode 14: [0,0]\nThe edges are: (0,10) (0,13) (11,0) (14,0) (5,1) (1,14) (2,7) (14,2) (12,3) (11,3) (3,14) (6,4) (4,7) (10,4) (8,5) (9,6) (7,11) (9,8) (8,12) (9,10) (11,13) (13,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,7]\nnode 1: [3,4]\nnode 2: [4,3]\nnode 3: [4,5]\nnode 4: [4,4]\nnode 5: [2,2]\nnode 6: [0,4]\nnode 7: [1,5]\nnode 8: [2,5]\nnode 9: [3,4]\nnode 10: [1,5]\nnode 11: [3,3]\nnode 12: [1,2]\nnode 13: [3,4]\nnode 14: [2,3]." - } - ] - }, - { - "id": "gnn-hard-graph740", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [1,0]\nnode 10: [1,0]\nnode 11: [1,0]\nnode 12: [0,1]\nnode 13: [0,0]\nnode 14: [0,0]\nThe edges are: (0,11) (0,8) (0,6) (7,1) (10,1) (1,4) (8,1) (1,2) (14,2) (13,2) (12,2) (4,3) (3,6) (9,4) (4,7) (14,4) (4,12) (7,5) (5,14) (12,6) (13,7) (9,8) (8,10) (14,8) (13,8) (11,10) (14,12) (13,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,5]\nnode 1: [12,6]\nnode 2: [11,8]\nnode 3: [5,6]\nnode 4: [11,10]\nnode 5: [3,3]\nnode 6: [6,5]\nnode 7: [12,8]\nnode 8: [16,8]\nnode 9: [7,4]\nnode 10: [8,4]\nnode 11: [6,1]\nnode 12: [11,11]\nnode 13: [7,5]\nnode 14: [11,8]." - } - ] - }, - { - "id": "gnn-hard-graph205", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [1,1]\nnode 9: [1,1]\nThe edges are: (9,0) (0,7) (2,1) (1,9) (2,5) (3,6) (3,8) (6,4) (7,5) (8,5) (6,8) (9,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,4]\nnode 1: [2,4]\nnode 2: [4,3]\nnode 3: [2,6]\nnode 4: [1,3]\nnode 5: [3,7]\nnode 6: [4,6]\nnode 7: [4,6]\nnode 8: [5,7]\nnode 9: [4,5]." - } - ] - }, - { - "id": "gnn-hard-graph365", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [0,1]\nnode 10: [0,1]\nnode 11: [1,0]\nThe edges are: (11,0) (1,2) (2,7) (2,5) (7,3) (3,5) (9,4) (11,5) (8,5) (6,9) (7,6) (10,9) (11,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,2]\nnode 1: [1,1]\nnode 2: [6,5]\nnode 3: [5,4]\nnode 4: [3,2]\nnode 5: [2,3]\nnode 6: [5,4]\nnode 7: [3,2]\nnode 8: [3,2]\nnode 9: [1,5]\nnode 10: [3,2]\nnode 11: [7,4]." - } - ] - }, - { - "id": "gnn-hard-graph447", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [1,1]\nnode 10: [0,0]\nnode 11: [1,0]\nThe edges are: (0,8) (0,5) (3,1) (1,9) (7,2) (2,5) (4,2) (9,2) (10,4) (5,7) (9,5) (8,6) (11,7) (9,10) (11,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,3]\nnode 1: [1,1]\nnode 2: [6,6]\nnode 3: [2,2]\nnode 4: [5,3]\nnode 5: [7,4]\nnode 6: [1,0]\nnode 7: [7,6]\nnode 8: [1,0]\nnode 9: [10,8]\nnode 10: [2,3]\nnode 11: [4,2]." - } - ] - }, - { - "id": "gnn-hard-graph363", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [1,0]\nnode 10: [0,0]\nnode 11: [0,0]\nThe edges are: (5,0) (0,9) (3,1) (4,1) (2,11) (2,6) (8,2) (2,4) (3,6) (3,8) (4,3) (7,4) (8,4) (4,5) (5,6) (5,10) (8,5) (9,8) (9,11) (11,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,5]\nnode 1: [6,6]\nnode 2: [12,12]\nnode 3: [12,13]\nnode 4: [14,14]\nnode 5: [11,13]\nnode 6: [7,7]\nnode 7: [4,4]\nnode 8: [13,13]\nnode 9: [7,6]\nnode 10: [5,4]\nnode 11: [4,5]." - } - ] - }, - { - "id": "gnn-hard-graph108", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [1,0]\nThe edges are: (0,5) (0,8) (4,1) (8,1) (1,3) (5,2) (4,2) (6,5) (7,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [1,4]\nnode 2: [2,3]\nnode 3: [3,2]\nnode 4: [5,4]\nnode 5: [5,5]\nnode 6: [1,1]\nnode 7: [1,2]\nnode 8: [5,3]." - } - ] - }, - { - "id": "gnn-hard-graph772", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [0,1]\nnode 11: [1,1]\nnode 12: [1,1]\nnode 13: [1,0]\nnode 14: [0,0]\nThe edges are: (11,0) (0,2) (5,1) (1,9) (3,1) (1,6) (2,10) (2,13) (2,14) (9,2) (2,3) (4,3) (9,4) (14,5) (5,11) (7,6) (6,14) (6,11) (10,7) (13,7) (7,14) (11,8) (10,14) (12,13) (14,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,4]\nnode 1: [8,5]\nnode 2: [9,9]\nnode 3: [3,2]\nnode 4: [4,2]\nnode 5: [7,5]\nnode 6: [9,6]\nnode 7: [6,8]\nnode 8: [2,2]\nnode 9: [3,2]\nnode 10: [6,6]\nnode 11: [6,5]\nnode 12: [4,5]\nnode 13: [4,3]\nnode 14: [8,7]." - } - ] - }, - { - "id": "gnn-hard-graph125", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [1,1]\nThe edges are: (0,9) (6,1) (2,1) (2,3) (5,2) (7,2) (3,9) (4,3) (5,3) (4,9) (7,5) (8,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [4,3]\nnode 2: [5,10]\nnode 3: [8,6]\nnode 4: [5,5]\nnode 5: [7,8]\nnode 6: [0,3]\nnode 7: [4,4]\nnode 8: [1,1]\nnode 9: [6,6]." - } - ] - }, - { - "id": "gnn-hard-graph402", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [0,1]\nThe edges are: (6,0) (7,0) (1,7) (10,2) (7,3) (4,5) (4,9) (6,10) (7,8) (7,10) (11,9) (11,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,6]\nnode 1: [2,4]\nnode 2: [2,3]\nnode 3: [2,4]\nnode 4: [0,1]\nnode 5: [1,2]\nnode 6: [3,5]\nnode 7: [6,8]\nnode 8: [2,4]\nnode 9: [2,4]\nnode 10: [6,9]\nnode 11: [2,4]." - } - ] - }, - { - "id": "gnn-hard-graph286", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [1,0]\nnode 10: [1,1]\nThe edges are: (0,4) (0,9) (0,3) (6,0) (9,1) (1,7) (2,5) (3,9) (8,4) (6,4) (5,8) (8,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,6]\nnode 1: [1,3]\nnode 2: [0,1]\nnode 3: [5,3]\nnode 4: [8,4]\nnode 5: [4,3]\nnode 6: [5,3]\nnode 7: [2,0]\nnode 8: [1,3]\nnode 9: [7,2]\nnode 10: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph583", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [1,0]\nnode 11: [0,1]\nnode 12: [0,1]\nThe edges are: (0,8) (1,0) (0,2) (9,1) (2,1) (10,1) (5,3) (12,4) (4,9) (10,4) (4,5) (10,5) (11,5) (8,6) (7,12) (8,9) (9,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,7]\nnode 1: [6,7]\nnode 2: [5,5]\nnode 3: [1,2]\nnode 4: [4,6]\nnode 5: [2,3]\nnode 6: [2,2]\nnode 7: [1,1]\nnode 8: [3,4]\nnode 9: [7,8]\nnode 10: [5,7]\nnode 11: [1,2]\nnode 12: [2,5]." - } - ] - }, - { - "id": "gnn-hard-graph223", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [1,0]\nThe edges are: (2,0) (6,0) (0,1) (5,1) (8,1) (1,4) (3,5) (6,3) (8,4) (4,7) (6,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,2]\nnode 1: [6,4]\nnode 2: [2,1]\nnode 3: [4,2]\nnode 4: [6,3]\nnode 5: [6,2]\nnode 6: [5,3]\nnode 7: [2,1]\nnode 8: [6,2]\nnode 9: [3,1]." - } - ] - }, - { - "id": "gnn-hard-graph628", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [1,1]\nnode 9: [1,1]\nnode 10: [1,1]\nnode 11: [1,0]\nnode 12: [0,0]\nnode 13: [0,1]\nThe edges are: (0,10) (2,1) (1,7) (2,11) (2,9) (2,13) (6,3) (3,7) (3,8) (4,6) (4,12) (8,4) (6,5) (5,13) (6,9) (7,11) (9,8) (10,11) (11,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [5,3]\nnode 2: [4,10]\nnode 3: [7,5]\nnode 4: [6,4]\nnode 5: [5,3]\nnode 6: [3,10]\nnode 7: [2,9]\nnode 8: [3,8]\nnode 9: [8,6]\nnode 10: [2,5]\nnode 11: [9,5]\nnode 12: [1,2]\nnode 13: [4,8]." - } - ] - }, - { - "id": "gnn-hard-graph472", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [0,0]\nThe edges are: (11,0) (10,0) (1,3) (8,1) (5,2) (3,2) (2,6) (9,2) (7,2) (9,3) (10,3) (11,4) (5,11) (10,6) (8,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,4]\nnode 1: [2,4]\nnode 2: [8,10]\nnode 3: [7,11]\nnode 4: [1,1]\nnode 5: [3,5]\nnode 6: [4,7]\nnode 7: [2,5]\nnode 8: [2,4]\nnode 9: [4,7]\nnode 10: [5,6]\nnode 11: [2,2]." - } - ] - }, - { - "id": "gnn-hard-graph565", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,1]\nnode 10: [1,0]\nnode 11: [1,0]\nnode 12: [0,0]\nThe edges are: (12,0) (0,9) (10,0) (11,0) (1,9) (8,1) (12,2) (9,2) (2,11) (12,3) (4,3) (11,5) (7,5) (9,6) (11,6) (6,8) (8,11) (12,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,6]\nnode 1: [2,2]\nnode 2: [4,6]\nnode 3: [3,3]\nnode 4: [0,1]\nnode 5: [1,4]\nnode 6: [3,5]\nnode 7: [1,1]\nnode 8: [2,7]\nnode 9: [6,8]\nnode 10: [2,1]\nnode 11: [6,6]\nnode 12: [4,4]." - } - ] - }, - { - "id": "gnn-hard-graph350", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [1,0]\nnode 10: [1,0]\nThe edges are: (8,0) (1,0) (10,0) (6,1) (2,1) (1,3) (10,2) (6,3) (4,3) (3,10) (4,5) (4,10) (9,4) (9,7) (8,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [6,5]\nnode 1: [5,1]\nnode 2: [5,4]\nnode 3: [9,6]\nnode 4: [8,3]\nnode 5: [3,1]\nnode 6: [4,2]\nnode 7: [2,1]\nnode 8: [4,2]\nnode 9: [4,1]\nnode 10: [8,2]." - } - ] - }, - { - "id": "gnn-hard-graph63", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [1,1]\nThe edges are: (0,7) (1,0) (2,0) (1,8) (6,2) (8,3) (6,4) (5,4) (5,6) (8,5) (8,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,4]\nnode 1: [3,4]\nnode 2: [3,4]\nnode 3: [3,2]\nnode 4: [6,3]\nnode 5: [8,5]\nnode 6: [10,5]\nnode 7: [0,2]\nnode 8: [9,6]." - } - ] - }, - { - "id": "gnn-hard-graph284", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [0,1]\nnode 10: [1,0]\nThe edges are: (6,0) (4,0) (10,0) (9,0) (1,3) (6,2) (3,4) (8,3) (7,5) (10,5) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,6]\nnode 1: [2,2]\nnode 2: [1,2]\nnode 3: [2,4]\nnode 4: [4,5]\nnode 5: [2,2]\nnode 6: [3,4]\nnode 7: [3,1]\nnode 8: [3,3]\nnode 9: [2,3]\nnode 10: [4,3]." - } - ] - }, - { - "id": "gnn-hard-graph808", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [1,0]\nnode 9: [0,0]\nnode 10: [1,1]\nnode 11: [1,0]\nnode 12: [0,1]\nnode 13: [1,0]\nnode 14: [0,0]\nThe edges are: (1,0) (0,7) (14,0) (6,1) (6,2) (2,13) (4,2) (14,2) (8,3) (3,5) (4,9) (11,4) (10,4) (5,11) (6,12) (6,14) (11,8) (14,8) (9,13) (9,14) (14,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,4]\nnode 1: [1,2]\nnode 2: [4,8]\nnode 3: [4,2]\nnode 4: [8,1]\nnode 5: [5,0]\nnode 6: [4,6]\nnode 7: [1,0]\nnode 8: [7,3]\nnode 9: [4,6]\nnode 10: [4,5]\nnode 11: [6,4]\nnode 12: [0,2]\nnode 13: [4,1]\nnode 14: [8,4]." - } - ] - }, - { - "id": "gnn-hard-graph609", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [1,0]\nnode 9: [0,0]\nnode 10: [1,0]\nnode 11: [1,0]\nnode 12: [0,1]\nnode 13: [1,0]\nThe edges are: (13,0) (1,11) (10,1) (9,1) (5,1) (2,4) (2,12) (11,3) (3,7) (8,4) (5,8) (6,12) (11,8) (8,13) (9,10) (11,10) (10,13) (11,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,0]\nnode 1: [11,5]\nnode 2: [2,1]\nnode 3: [5,2]\nnode 4: [5,1]\nnode 5: [7,0]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [10,3]\nnode 9: [6,1]\nnode 10: [12,3]\nnode 11: [12,2]\nnode 12: [5,4]\nnode 13: [8,1]." - } - ] - }, - { - "id": "gnn-hard-graph397", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [1,1]\nnode 10: [1,0]\nnode 11: [0,0]\nThe edges are: (0,7) (11,0) (0,2) (0,9) (1,0) (6,1) (10,2) (2,9) (3,4) (3,7) (3,5) (11,3) (8,4) (5,6) (5,9) (6,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [12,10]\nnode 1: [6,3]\nnode 2: [7,6]\nnode 3: [10,6]\nnode 4: [1,1]\nnode 5: [5,5]\nnode 6: [8,6]\nnode 7: [7,4]\nnode 8: [2,1]\nnode 9: [10,6]\nnode 10: [3,2]\nnode 11: [5,3]." - } - ] - }, - { - "id": "gnn-hard-graph67", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [1,0]\nThe edges are: (3,0) (8,0) (7,0) (1,8) (6,2) (3,4) (3,7) (3,5) (4,6) (5,4) (8,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,4]\nnode 1: [1,2]\nnode 2: [2,1]\nnode 3: [4,6]\nnode 4: [6,3]\nnode 5: [4,4]\nnode 6: [2,6]\nnode 7: [4,2]\nnode 8: [4,2]." - } - ] - }, - { - "id": "gnn-hard-graph758", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [1,0]\nnode 11: [1,0]\nnode 12: [1,1]\nnode 13: [0,1]\nnode 14: [1,0]\nThe edges are: (2,0) (11,0) (3,1) (1,6) (11,1) (3,4) (3,8) (5,3) (4,9) (12,4) (9,5) (13,5) (5,12) (6,5) (6,14) (8,7) (7,10) (11,7) (13,9) (12,9) (9,11) (10,13) (13,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,5]\nnode 1: [4,8]\nnode 2: [1,0]\nnode 3: [5,6]\nnode 4: [6,10]\nnode 5: [12,13]\nnode 6: [3,3]\nnode 7: [1,7]\nnode 8: [3,4]\nnode 9: [11,14]\nnode 10: [6,3]\nnode 11: [11,7]\nnode 12: [7,9]\nnode 13: [6,13]\nnode 14: [2,1]." - } - ] - }, - { - "id": "gnn-hard-graph508", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [1,1]\nnode 9: [0,1]\nnode 10: [0,1]\nnode 11: [0,0]\nnode 12: [0,0]\nThe edges are: (11,0) (0,10) (0,9) (11,1) (2,1) (3,2) (5,2) (6,2) (3,5) (8,4) (4,7) (5,12) (6,5) (8,10) (11,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,5]\nnode 1: [4,5]\nnode 2: [6,6]\nnode 3: [6,6]\nnode 4: [0,3]\nnode 5: [5,5]\nnode 6: [6,6]\nnode 7: [1,2]\nnode 8: [2,4]\nnode 9: [0,2]\nnode 10: [0,4]\nnode 11: [1,3]\nnode 12: [4,5]." - } - ] - }, - { - "id": "gnn-hard-graph645", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [0,1]\nnode 10: [0,1]\nnode 11: [1,1]\nnode 12: [1,0]\nnode 13: [1,0]\nThe edges are: (8,0) (0,9) (10,0) (1,11) (1,4) (2,12) (3,11) (4,3) (9,3) (11,4) (8,5) (5,9) (5,13) (11,6) (6,13) (7,10) (11,8) (9,12) (9,13) (10,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,4]\nnode 1: [5,5]\nnode 2: [1,1]\nnode 3: [9,7]\nnode 4: [4,6]\nnode 5: [6,8]\nnode 6: [2,7]\nnode 7: [2,0]\nnode 8: [3,8]\nnode 9: [3,12]\nnode 10: [0,8]\nnode 11: [9,8]\nnode 12: [5,2]\nnode 13: [9,5]." - } - ] - }, - { - "id": "gnn-hard-graph358", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [1,0]\nnode 10: [0,1]\nThe edges are: (3,0) (2,0) (1,10) (2,1) (2,3) (2,7) (9,2) (7,3) (4,9) (6,5) (6,8) (7,8) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [6,5]\nnode 1: [5,2]\nnode 2: [5,10]\nnode 3: [6,5]\nnode 4: [1,2]\nnode 5: [0,2]\nnode 6: [1,1]\nnode 7: [7,6]\nnode 8: [1,4]\nnode 9: [6,2]\nnode 10: [1,4]." - } - ] - }, - { - "id": "gnn-hard-graph222", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [0,0]\nThe edges are: (0,1) (1,9) (3,1) (4,2) (8,2) (2,5) (9,3) (3,5) (5,6) (6,7) (8,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [2,3]\nnode 2: [3,5]\nnode 3: [5,4]\nnode 4: [3,0]\nnode 5: [7,2]\nnode 6: [4,5]\nnode 7: [3,1]\nnode 8: [6,1]\nnode 9: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph668", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [1,0]\nnode 12: [1,1]\nnode 13: [0,0]\nThe edges are: (13,0) (9,0) (8,1) (8,2) (2,6) (5,2) (10,3) (3,9) (3,5) (8,4) (5,11) (6,7) (9,6) (9,7) (12,8) (8,13) (11,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,5]\nnode 1: [4,3]\nnode 2: [8,7]\nnode 3: [5,4]\nnode 4: [4,3]\nnode 5: [7,8]\nnode 6: [7,8]\nnode 7: [5,6]\nnode 8: [10,10]\nnode 9: [5,9]\nnode 10: [2,3]\nnode 11: [6,4]\nnode 12: [4,3]\nnode 13: [4,4]." - } - ] - }, - { - "id": "gnn-hard-graph520", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [0,0]\nnode 12: [1,1]\nThe edges are: (0,11) (9,0) (1,9) (3,1) (2,11) (5,2) (2,10) (3,2) (4,3) (12,3) (3,10) (9,3) (8,4) (5,6) (6,10) (6,8) (12,7) (11,7) (12,9) (9,11) (10,11) (11,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,9]\nnode 1: [7,8]\nnode 2: [14,12]\nnode 3: [14,15]\nnode 4: [6,5]\nnode 5: [6,4]\nnode 6: [7,4]\nnode 7: [7,8]\nnode 8: [5,4]\nnode 9: [12,15]\nnode 10: [15,13]\nnode 11: [12,13]\nnode 12: [13,14]." - } - ] - }, - { - "id": "gnn-hard-graph368", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [0,0]\nnode 10: [0,0]\nnode 11: [0,0]\nThe edges are: (5,0) (0,10) (1,0) (1,5) (1,10) (1,4) (1,3) (2,6) (3,6) (5,11) (7,5) (6,8) (7,8) (8,10) (8,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,6]\nnode 1: [7,8]\nnode 2: [3,2]\nnode 3: [5,3]\nnode 4: [2,1]\nnode 5: [4,3]\nnode 6: [4,1]\nnode 7: [2,2]\nnode 8: [7,7]\nnode 9: [1,0]\nnode 10: [4,2]\nnode 11: [1,2]." - } - ] - }, - { - "id": "gnn-hard-graph20", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [1,0]\nThe edges are: (0,6) (5,0) (2,0) (1,4) (3,1) (5,2) (2,7) (4,2) (2,8) (3,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,6]\nnode 1: [2,2]\nnode 2: [6,4]\nnode 3: [1,1]\nnode 4: [2,5]\nnode 5: [3,6]\nnode 6: [1,2]\nnode 7: [2,4]\nnode 8: [3,5]." - } - ] - }, - { - "id": "gnn-hard-graph34", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [1,0]\nThe edges are: (0,3) (0,5) (7,1) (3,1) (1,8) (1,5) (7,2) (2,6) (2,5) (3,6) (4,7) (7,6) (6,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,6]\nnode 1: [5,11]\nnode 2: [4,8]\nnode 3: [4,6]\nnode 4: [2,3]\nnode 5: [4,6]\nnode 6: [5,10]\nnode 7: [4,6]\nnode 8: [3,4]." - } - ] - }, - { - "id": "gnn-hard-graph28", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [0,0]\nThe edges are: (0,3) (0,5) (1,7) (5,1) (4,2) (3,2) (7,2) (3,5) (8,3) (5,4) (6,4) (6,5) (5,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,4]\nnode 1: [2,4]\nnode 2: [5,6]\nnode 3: [4,7]\nnode 4: [4,4]\nnode 5: [9,10]\nnode 6: [3,4]\nnode 7: [2,2]\nnode 8: [3,4]." - } - ] - }, - { - "id": "gnn-hard-graph601", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [0,1]\nnode 11: [0,1]\nnode 12: [1,1]\nnode 13: [0,0]\nThe edges are: (8,0) (0,4) (0,2) (1,4) (2,4) (6,3) (8,4) (13,4) (4,12) (7,5) (8,6) (7,11) (7,9) (8,10) (9,13) (10,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,10]\nnode 1: [1,5]\nnode 2: [1,8]\nnode 3: [1,1]\nnode 4: [0,12]\nnode 5: [0,2]\nnode 6: [0,3]\nnode 7: [0,3]\nnode 8: [3,11]\nnode 9: [0,3]\nnode 10: [0,5]\nnode 11: [0,2]\nnode 12: [2,7]\nnode 13: [1,6]." - } - ] - }, - { - "id": "gnn-hard-graph452", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [1,0]\nnode 11: [1,1]\nThe edges are: (3,0) (0,6) (0,9) (1,6) (1,8) (4,1) (1,2) (2,3) (2,5) (7,2) (4,9) (5,4) (5,10) (7,10) (11,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [5,9]\nnode 2: [6,2]\nnode 3: [4,6]\nnode 4: [3,2]\nnode 5: [5,7]\nnode 6: [3,5]\nnode 7: [3,4]\nnode 8: [1,3]\nnode 9: [4,6]\nnode 10: [4,0]\nnode 11: [1,2]." - } - ] - }, - { - "id": "gnn-hard-graph301", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [0,0]\nnode 10: [1,1]\nThe edges are: (0,1) (0,7) (0,10) (0,9) (9,1) (5,2) (10,3) (3,4) (10,4) (9,4) (8,5) (5,10) (6,8) (9,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,1]\nnode 1: [6,1]\nnode 2: [1,1]\nnode 3: [4,3]\nnode 4: [7,2]\nnode 5: [2,1]\nnode 6: [0,0]\nnode 7: [6,1]\nnode 8: [1,1]\nnode 9: [5,3]\nnode 10: [8,5]." - } - ] - }, - { - "id": "gnn-hard-graph490", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [1,1]\nnode 10: [0,1]\nnode 11: [0,1]\nnode 12: [0,1]\nThe edges are: (1,0) (7,0) (0,11) (0,5) (1,9) (3,1) (8,1) (1,11) (5,1) (2,10) (6,2) (11,2) (5,2) (6,3) (12,3) (8,4) (9,5) (7,5) (5,6) (5,12) (12,6) (12,7) (8,10) (11,8) (12,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [9,9]\nnode 1: [10,14]\nnode 2: [9,9]\nnode 3: [11,7]\nnode 4: [1,3]\nnode 5: [17,14]\nnode 6: [12,13]\nnode 7: [11,10]\nnode 8: [5,4]\nnode 9: [12,10]\nnode 10: [3,6]\nnode 11: [8,10]\nnode 12: [10,11]." - } - ] - }, - { - "id": "gnn-hard-graph165", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [0,1]\nThe edges are: (0,2) (0,3) (2,1) (1,5) (1,7) (6,2) (8,2) (4,2) (3,6) (3,4) (5,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,6]\nnode 1: [4,7]\nnode 2: [0,4]\nnode 3: [0,3]\nnode 4: [2,6]\nnode 5: [0,2]\nnode 6: [2,6]\nnode 7: [0,1]\nnode 8: [2,4]\nnode 9: [1,2]." - } - ] - }, - { - "id": "gnn-hard-graph635", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [1,1]\nnode 11: [1,1]\nnode 12: [0,0]\nnode 13: [0,0]\nThe edges are: (3,0) (0,5) (0,9) (1,12) (1,2) (1,9) (6,2) (12,2) (2,13) (5,2) (3,12) (3,13) (4,6) (10,4) (4,5) (5,13) (6,12) (10,6) (7,8) (8,12) (12,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,3]\nnode 1: [7,7]\nnode 2: [8,13]\nnode 3: [8,8]\nnode 4: [2,6]\nnode 5: [9,8]\nnode 6: [7,9]\nnode 7: [1,1]\nnode 8: [3,5]\nnode 9: [4,4]\nnode 10: [3,5]\nnode 11: [3,4]\nnode 12: [6,8]\nnode 13: [4,4]." - } - ] - }, - { - "id": "gnn-hard-graph1", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [0,0]\nnode 8: [1,1]\nThe edges are: (0,7) (0,8) (1,2) (1,8) (4,1) (2,8) (6,3) (7,3) (3,8) (5,3) (6,4) (5,6) (8,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,6]\nnode 1: [6,5]\nnode 2: [5,5]\nnode 3: [5,10]\nnode 4: [4,4]\nnode 5: [3,5]\nnode 6: [5,6]\nnode 7: [5,7]\nnode 8: [9,10]." - } - ] - }, - { - "id": "gnn-hard-graph5", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [0,0]\nThe edges are: (1,0) (1,3) (6,1) (7,2) (2,6) (7,3) (3,6) (3,8) (6,4) (6,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,0]\nnode 1: [8,5]\nnode 2: [5,3]\nnode 3: [6,3]\nnode 4: [4,2]\nnode 5: [4,2]\nnode 6: [8,3]\nnode 7: [5,3]\nnode 8: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph0", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [1,1]\nThe edges are: (8,0) (0,6) (0,5) (1,7) (5,1) (3,1) (2,8) (4,6) (8,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,4]\nnode 1: [4,2]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [3,3]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [4,4]." - } - ] - }, - { - "id": "gnn-hard-graph604", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [1,0]\nnode 10: [1,0]\nnode 11: [0,0]\nnode 12: [1,0]\nnode 13: [0,1]\nThe edges are: (0,7) (0,10) (1,8) (1,2) (2,12) (3,5) (12,3) (4,5) (11,4) (4,10) (5,13) (6,12) (7,8) (9,8) (9,11) (10,11) (12,10) (13,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,3]\nnode 1: [2,2]\nnode 2: [2,2]\nnode 3: [3,2]\nnode 4: [6,3]\nnode 5: [2,3]\nnode 6: [2,1]\nnode 7: [2,1]\nnode 8: [0,4]\nnode 9: [4,2]\nnode 10: [7,3]\nnode 11: [3,4]\nnode 12: [5,3]\nnode 13: [4,2]." - } - ] - }, - { - "id": "gnn-hard-graph485", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [1,0]\nnode 9: [1,0]\nnode 10: [1,0]\nnode 11: [0,1]\nnode 12: [1,0]\nThe edges are: (0,5) (3,1) (2,1) (4,1) (5,2) (7,2) (2,12) (8,2) (11,2) (12,3) (3,10) (4,11) (5,6) (10,6) (8,7) (7,9) (7,11) (8,12) (9,12) (11,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [5,3]\nnode 2: [7,7]\nnode 3: [2,2]\nnode 4: [1,3]\nnode 5: [6,2]\nnode 6: [1,1]\nnode 7: [6,6]\nnode 8: [7,4]\nnode 9: [4,2]\nnode 10: [4,0]\nnode 11: [7,5]\nnode 12: [8,6]." - } - ] - }, - { - "id": "gnn-hard-graph681", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [1,0]\nnode 9: [1,1]\nnode 10: [1,0]\nnode 11: [1,0]\nnode 12: [1,1]\nnode 13: [0,1]\nThe edges are: (0,4) (1,0) (8,0) (6,0) (2,5) (3,11) (13,3) (3,9) (9,4) (4,6) (8,5) (7,5) (5,12) (5,6) (8,6) (11,7) (8,12) (10,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [9,4]\nnode 1: [2,0]\nnode 2: [5,1]\nnode 3: [5,3]\nnode 4: [5,2]\nnode 5: [7,6]\nnode 6: [13,4]\nnode 7: [7,2]\nnode 8: [10,3]\nnode 9: [5,3]\nnode 10: [2,1]\nnode 11: [3,3]\nnode 12: [8,3]\nnode 13: [2,3]." - } - ] - }, - { - "id": "gnn-hard-graph168", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [1,1]\nThe edges are: (4,0) (5,0) (4,1) (3,1) (2,6) (4,2) (3,4) (4,5) (8,4) (5,7) (7,6) (9,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,6]\nnode 1: [5,6]\nnode 2: [5,4]\nnode 3: [5,6]\nnode 4: [3,9]\nnode 5: [6,6]\nnode 6: [3,2]\nnode 7: [1,2]\nnode 8: [4,4]\nnode 9: [2,1]." - } - ] - }, - { - "id": "gnn-hard-graph293", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [1,0]\nnode 10: [1,0]\nThe edges are: (0,1) (0,5) (0,7) (1,3) (2,9) (2,8) (4,3) (3,9) (8,3) (4,5) (5,10) (6,10) (7,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,4]\nnode 1: [2,4]\nnode 2: [2,2]\nnode 3: [3,3]\nnode 4: [2,5]\nnode 5: [3,1]\nnode 6: [1,1]\nnode 7: [2,1]\nnode 8: [2,4]\nnode 9: [2,4]\nnode 10: [2,2]." - } - ] - }, - { - "id": "gnn-hard-graph420", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [1,0]\nnode 10: [0,1]\nnode 11: [0,1]\nThe edges are: (0,8) (0,10) (1,10) (1,9) (2,9) (6,3) (3,7) (11,4) (9,5) (6,10) (8,7) (7,9) (11,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,4]\nnode 1: [5,3]\nnode 2: [3,0]\nnode 3: [2,4]\nnode 4: [0,1]\nnode 5: [3,0]\nnode 6: [3,4]\nnode 7: [6,2]\nnode 8: [3,4]\nnode 9: [5,3]\nnode 10: [2,6]\nnode 11: [2,4]." - } - ] - }, - { - "id": "gnn-hard-graph60", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [0,1]\nThe edges are: (3,0) (8,0) (0,4) (0,1) (0,6) (1,2) (3,2) (4,2) (3,7) (5,3) (4,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,2]\nnode 1: [4,4]\nnode 2: [4,2]\nnode 3: [6,4]\nnode 4: [5,4]\nnode 5: [2,1]\nnode 6: [2,3]\nnode 7: [2,1]\nnode 8: [3,4]." - } - ] - }, - { - "id": "gnn-hard-graph390", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [1,0]\nnode 10: [1,0]\nnode 11: [1,0]\nThe edges are: (2,0) (0,3) (0,8) (7,0) (1,2) (1,10) (7,1) (11,2) (2,4) (2,9) (3,5) (4,3) (4,6) (7,4) (9,5) (5,7) (7,11) (11,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [12,6]\nnode 1: [11,3]\nnode 2: [8,3]\nnode 3: [4,2]\nnode 4: [12,5]\nnode 5: [7,5]\nnode 6: [1,1]\nnode 7: [8,2]\nnode 8: [2,1]\nnode 9: [6,1]\nnode 10: [4,0]\nnode 11: [11,3]." - } - ] - }, - { - "id": "gnn-hard-graph458", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [0,0]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,0]\nnode 7: [0,0]\nnode 8: [0,0]\nnode 9: [0,0]\nnode 10: [1,0]\nnode 11: [1,1]\nThe edges are: (0,3) (0,11) (7,1) (4,1) (8,2) (2,11) (3,5) (4,9) (4,8) (10,4) (10,6) (7,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [2,2]\nnode 2: [2,0]\nnode 3: [3,3]\nnode 4: [5,0]\nnode 5: [1,1]\nnode 6: [2,0]\nnode 7: [3,0]\nnode 8: [2,2]\nnode 9: [1,1]\nnode 10: [3,2]\nnode 11: [3,3]." - } - ] - }, - { - "id": "gnn-hard-graph2", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [1,1]\nThe edges are: (0,4) (7,0) (0,8) (1,7) (2,7) (5,2) (7,3) (3,8) (7,5) (6,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,4]\nnode 1: [2,3]\nnode 2: [4,4]\nnode 3: [3,4]\nnode 4: [3,3]\nnode 5: [3,5]\nnode 6: [2,3]\nnode 7: [10,10]\nnode 8: [5,5]." - } - ] - }, - { - "id": "gnn-hard-graph649", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,0]\nnode 8: [1,0]\nnode 9: [0,1]\nnode 10: [0,0]\nnode 11: [1,0]\nnode 12: [0,1]\nnode 13: [0,0]\nThe edges are: (12,0) (0,8) (13,0) (4,1) (2,1) (12,1) (1,6) (1,3) (7,2) (2,5) (2,10) (8,2) (13,2) (3,4) (3,5) (4,13) (6,5) (9,11) (13,9) (10,13) (13,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,7]\nnode 1: [2,2]\nnode 2: [4,13]\nnode 3: [3,6]\nnode 4: [4,7]\nnode 5: [2,0]\nnode 6: [3,5]\nnode 7: [1,0]\nnode 8: [2,1]\nnode 9: [1,5]\nnode 10: [2,4]\nnode 11: [1,0]\nnode 12: [4,8]\nnode 13: [3,4]." - } - ] - }, - { - "id": "gnn-hard-graph211", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [1,1]\nThe edges are: (6,0) (0,4) (0,1) (6,1) (1,3) (9,1) (6,2) (3,6) (7,3) (6,4) (5,6) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,4]\nnode 1: [7,1]\nnode 2: [2,1]\nnode 3: [3,4]\nnode 4: [4,1]\nnode 5: [2,1]\nnode 6: [5,3]\nnode 7: [3,0]\nnode 8: [0,1]\nnode 9: [1,2]." - } - ] - }, - { - "id": "gnn-hard-graph13", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,1]\nThe edges are: (5,0) (3,0) (0,4) (8,1) (1,7) (1,2) (2,6) (2,4) (7,3) (6,5) (8,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,1]\nnode 1: [5,3]\nnode 2: [2,3]\nnode 3: [5,1]\nnode 4: [5,1]\nnode 5: [4,1]\nnode 6: [4,2]\nnode 7: [1,3]\nnode 8: [1,3]." - } - ] - }, - { - "id": "gnn-hard-graph136", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [0,0]\nnode 9: [1,0]\nThe edges are: (0,4) (9,0) (2,0) (1,5) (1,4) (1,9) (2,8) (9,2) (3,5) (5,6) (7,6) (8,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [2,4]\nnode 2: [5,3]\nnode 3: [1,2]\nnode 4: [6,2]\nnode 5: [5,2]\nnode 6: [2,3]\nnode 7: [2,2]\nnode 8: [2,1]\nnode 9: [7,2]." - } - ] - }, - { - "id": "gnn-hard-graph399", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [0,0]\nnode 10: [1,0]\nnode 11: [0,0]\nThe edges are: (0,9) (0,3) (2,0) (11,1) (1,3) (1,8) (2,1) (3,2) (8,2) (9,3) (10,3) (8,3) (11,4) (5,4) (9,6) (7,6) (8,6) (8,7) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [12,7]\nnode 1: [14,8]\nnode 2: [14,7]\nnode 3: [17,11]\nnode 4: [1,2]\nnode 5: [1,1]\nnode 6: [8,5]\nnode 7: [6,4]\nnode 8: [15,10]\nnode 9: [10,6]\nnode 10: [8,4]\nnode 11: [4,3]." - } - ] - }, - { - "id": "gnn-hard-graph552", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [0,0]\nnode 9: [1,1]\nnode 10: [1,0]\nnode 11: [0,0]\nnode 12: [0,1]\nThe edges are: (0,2) (9,0) (1,0) (0,7) (1,3) (1,5) (1,7) (2,11) (2,7) (5,4) (5,12) (9,6) (6,8) (12,7) (7,10) (9,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,7]\nnode 1: [5,5]\nnode 2: [7,5]\nnode 3: [1,2]\nnode 4: [0,1]\nnode 5: [1,3]\nnode 6: [3,1]\nnode 7: [4,8]\nnode 8: [1,1]\nnode 9: [5,4]\nnode 10: [3,2]\nnode 11: [3,3]\nnode 12: [3,3]." - } - ] - }, - { - "id": "gnn-hard-graph22", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [0,1]\nThe edges are: (3,0) (0,4) (0,7) (4,1) (8,2) (3,7) (6,4) (5,6) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,4]\nnode 1: [1,2]\nnode 2: [1,1]\nnode 3: [4,3]\nnode 4: [2,5]\nnode 5: [0,2]\nnode 6: [1,3]\nnode 7: [5,4]\nnode 8: [2,2]." - } - ] - }, - { - "id": "gnn-hard-graph777", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [1,1]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [0,0]\nnode 12: [0,0]\nnode 13: [0,1]\nnode 14: [0,1]\nThe edges are: (0,5) (4,0) (0,14) (1,12) (1,3) (11,1) (3,2) (2,11) (7,2) (10,3) (9,3) (3,5) (3,13) (4,3) (12,3) (4,9) (13,4) (4,11) (7,4) (5,10) (9,5) (12,5) (6,5) (10,6) (6,13) (8,6) (6,7) (9,7) (7,13) (8,14) (11,8) (9,10) (13,9) (13,14)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,12]\nnode 1: [8,9]\nnode 2: [8,10]\nnode 3: [14,28]\nnode 4: [12,24]\nnode 5: [11,24]\nnode 6: [10,16]\nnode 7: [8,23]\nnode 8: [6,10]\nnode 9: [13,25]\nnode 10: [10,20]\nnode 11: [4,9]\nnode 12: [7,10]\nnode 13: [11,27]\nnode 14: [3,9]." - } - ] - }, - { - "id": "gnn-hard-graph602", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [1,0]\nnode 9: [1,1]\nnode 10: [0,1]\nnode 11: [0,0]\nnode 12: [0,0]\nnode 13: [0,1]\nThe edges are: (0,10) (1,13) (4,1) (12,1) (2,11) (3,10) (3,9) (13,3) (3,8) (9,4) (5,4) (4,11) (5,9) (11,5) (5,12) (8,5) (5,7) (7,6) (11,8) (9,10) (13,10) (11,12) (13,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,3]\nnode 1: [7,3]\nnode 2: [4,0]\nnode 3: [9,5]\nnode 4: [12,3]\nnode 5: [15,3]\nnode 6: [1,0]\nnode 7: [5,1]\nnode 8: [10,4]\nnode 9: [11,8]\nnode 10: [7,6]\nnode 11: [11,3]\nnode 12: [11,3]\nnode 13: [7,8]." - } - ] - }, - { - "id": "gnn-hard-graph36", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,0]\nThe edges are: (0,5) (0,7) (1,3) (1,7) (7,2) (3,7) (3,4) (4,6) (4,5) (5,7) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,4]\nnode 1: [4,3]\nnode 2: [3,2]\nnode 3: [6,5]\nnode 4: [4,3]\nnode 5: [6,4]\nnode 6: [2,1]\nnode 7: [5,8]\nnode 8: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph270", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [1,0]\nnode 10: [0,1]\nThe edges are: (0,7) (5,0) (9,1) (1,7) (1,5) (9,2) (7,2) (2,8) (5,2) (9,3) (3,8) (10,4) (7,4) (6,4) (4,8) (4,5) (5,10) (6,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,3]\nnode 1: [6,6]\nnode 2: [7,8]\nnode 3: [3,5]\nnode 4: [6,5]\nnode 5: [8,8]\nnode 6: [4,7]\nnode 7: [8,8]\nnode 8: [7,7]\nnode 9: [8,4]\nnode 10: [4,6]." - } - ] - }, - { - "id": "gnn-hard-graph52", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [1,0]\nThe edges are: (0,6) (2,1) (1,8) (6,2) (3,2) (7,4) (4,8) (8,5) (5,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [4,4]\nnode 2: [3,1]\nnode 3: [1,2]\nnode 4: [4,2]\nnode 5: [5,3]\nnode 6: [2,4]\nnode 7: [1,1]\nnode 8: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph362", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [0,0]\nnode 10: [1,1]\nnode 11: [1,0]\nThe edges are: (9,0) (10,0) (1,0) (1,8) (1,5) (2,1) (9,2) (2,8) (3,9) (3,10) (4,6) (4,7) (11,4) (8,6) (10,9) (9,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [11,8]\nnode 1: [7,8]\nnode 2: [11,10]\nnode 3: [7,4]\nnode 4: [4,4]\nnode 5: [4,4]\nnode 6: [4,4]\nnode 7: [2,1]\nnode 8: [8,8]\nnode 9: [8,7]\nnode 10: [8,6]\nnode 11: [7,4]." - } - ] - }, - { - "id": "gnn-hard-graph793", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [0,0]\nnode 9: [1,1]\nnode 10: [1,0]\nnode 11: [1,1]\nnode 12: [1,1]\nnode 13: [1,0]\nnode 14: [1,0]\nThe edges are: (8,0) (1,8) (9,1) (7,2) (8,3) (3,10) (4,5) (7,4) (7,5) (5,6) (6,7) (7,14) (8,7) (13,7) (12,9) (13,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [2,2]\nnode 2: [4,0]\nnode 3: [2,1]\nnode 4: [5,0]\nnode 5: [4,0]\nnode 6: [5,0]\nnode 7: [3,2]\nnode 8: [6,1]\nnode 9: [2,2]\nnode 10: [1,0]\nnode 11: [1,1]\nnode 12: [1,1]\nnode 13: [5,0]\nnode 14: [4,0]." - } - ] - }, - { - "id": "gnn-hard-graph805", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [1,0]\nnode 10: [0,1]\nnode 11: [0,1]\nnode 12: [1,0]\nnode 13: [1,0]\nnode 14: [1,0]\nThe edges are: (11,0) (0,7) (4,1) (1,10) (1,5) (14,2) (7,2) (2,8) (2,13) (11,3) (3,12) (3,8) (10,4) (12,4) (13,4) (5,9) (6,13) (12,7) (11,10) (10,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,3]\nnode 1: [4,6]\nnode 2: [7,3]\nnode 3: [6,5]\nnode 4: [5,10]\nnode 5: [2,2]\nnode 6: [1,2]\nnode 7: [6,6]\nnode 8: [4,2]\nnode 9: [1,1]\nnode 10: [7,9]\nnode 11: [3,6]\nnode 12: [7,7]\nnode 13: [6,3]\nnode 14: [3,1]." - } - ] - }, - { - "id": "gnn-hard-graph112", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [0,0]\nThe edges are: (0,8) (0,2) (0,1) (6,0) (1,3) (4,1) (3,2) (2,7) (3,4) (6,3) (8,4) (6,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,3]\nnode 1: [4,1]\nnode 2: [3,1]\nnode 3: [3,2]\nnode 4: [4,3]\nnode 5: [1,1]\nnode 6: [3,1]\nnode 7: [0,0]\nnode 8: [2,0]." - } - ] - }, - { - "id": "gnn-hard-graph787", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [1,0]\nnode 9: [0,0]\nnode 10: [0,0]\nnode 11: [1,0]\nnode 12: [1,0]\nnode 13: [1,0]\nnode 14: [0,1]\nThe edges are: (4,0) (1,6) (14,1) (11,2) (3,9) (12,3) (4,3) (7,3) (11,3) (13,4) (12,4) (10,5) (14,5) (10,6) (6,12) (8,6) (6,7) (7,11) (11,8) (9,14) (10,12) (10,11) (14,10) (13,14)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [5,1]\nnode 2: [3,0]\nnode 3: [6,4]\nnode 4: [3,2]\nnode 5: [5,4]\nnode 6: [5,8]\nnode 7: [9,0]\nnode 8: [6,0]\nnode 9: [5,1]\nnode 10: [8,3]\nnode 11: [9,5]\nnode 12: [11,4]\nnode 13: [4,2]\nnode 14: [3,8]." - } - ] - }, - { - "id": "gnn-hard-graph99", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,1]\nThe edges are: (7,0) (2,0) (6,0) (0,8) (1,2) (1,6) (4,1) (2,7) (3,2) (8,2) (5,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,7]\nnode 1: [4,7]\nnode 2: [8,7]\nnode 3: [2,4]\nnode 4: [1,1]\nnode 5: [1,2]\nnode 6: [3,4]\nnode 7: [4,7]\nnode 8: [4,7]." - } - ] - }, - { - "id": "gnn-hard-graph445", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [1,0]\nnode 7: [0,0]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [0,0]\nThe edges are: (0,9) (6,0) (11,1) (10,1) (2,7) (2,4) (5,3) (9,3) (4,3) (3,10) (6,4) (5,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [2,0]\nnode 2: [1,2]\nnode 3: [2,1]\nnode 4: [5,6]\nnode 5: [4,5]\nnode 6: [2,2]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [4,5]\nnode 10: [4,5]\nnode 11: [1,1]." - } - ] - }, - { - "id": "gnn-hard-graph579", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [0,1]\nnode 10: [0,1]\nnode 11: [0,1]\nnode 12: [1,0]\nThe edges are: (0,5) (4,0) (7,0) (1,0) (5,1) (7,1) (1,11) (9,1) (3,2) (6,2) (7,3) (5,4) (7,4) (4,11) (4,9) (5,6) (6,8) (6,12) (7,6) (9,6) (9,7) (9,10) (12,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,11]\nnode 1: [2,11]\nnode 2: [4,5]\nnode 3: [0,4]\nnode 4: [2,11]\nnode 5: [6,12]\nnode 6: [1,12]\nnode 7: [8,16]\nnode 8: [3,4]\nnode 9: [6,14]\nnode 10: [1,5]\nnode 11: [2,6]\nnode 12: [4,5]." - } - ] - }, - { - "id": "gnn-hard-graph326", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [1,0]\nnode 10: [0,0]\nThe edges are: (10,0) (0,5) (4,0) (6,0) (7,1) (7,2) (6,3) (5,6) (7,5) (7,9) (8,10) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,6]\nnode 1: [1,2]\nnode 2: [1,2]\nnode 3: [1,2]\nnode 4: [2,1]\nnode 5: [4,5]\nnode 6: [4,2]\nnode 7: [1,1]\nnode 8: [1,2]\nnode 9: [2,4]\nnode 10: [2,1]." - } - ] - }, - { - "id": "gnn-hard-graph341", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [0,1]\nThe edges are: (3,0) (0,8) (9,0) (1,7) (5,1) (1,6) (2,3) (8,3) (8,4) (5,8) (8,6) (6,9) (10,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,7]\nnode 1: [3,2]\nnode 2: [1,2]\nnode 3: [2,6]\nnode 4: [2,3]\nnode 5: [3,5]\nnode 6: [4,7]\nnode 7: [1,2]\nnode 8: [3,7]\nnode 9: [1,3]\nnode 10: [1,2]." - } - ] - }, - { - "id": "gnn-hard-graph687", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [0,0]\nnode 8: [0,0]\nnode 9: [1,1]\nnode 10: [0,0]\nnode 11: [1,1]\nnode 12: [0,1]\nnode 13: [1,0]\nThe edges are: (0,3) (13,0) (11,0) (0,4) (1,2) (1,6) (8,2) (6,2) (4,10) (4,13) (4,5) (12,5) (6,11) (6,8) (7,13) (11,8) (9,8) (12,10) (11,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,8]\nnode 1: [5,5]\nnode 2: [9,9]\nnode 3: [4,3]\nnode 4: [8,9]\nnode 5: [5,4]\nnode 6: [10,11]\nnode 7: [2,2]\nnode 8: [7,8]\nnode 9: [4,4]\nnode 10: [5,4]\nnode 11: [13,12]\nnode 12: [4,7]\nnode 13: [8,5]." - } - ] - }, - { - "id": "gnn-hard-graph216", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [0,0]\nThe edges are: (1,0) (7,0) (8,0) (1,3) (5,1) (1,8) (2,4) (3,5) (9,4) (9,5) (6,9) (9,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,5]\nnode 1: [1,3]\nnode 2: [1,1]\nnode 3: [1,3]\nnode 4: [1,2]\nnode 5: [2,6]\nnode 6: [1,2]\nnode 7: [1,3]\nnode 8: [1,4]\nnode 9: [2,2]." - } - ] - }, - { - "id": "gnn-hard-graph384", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [1,1]\nnode 11: [0,0]\nThe edges are: (8,0) (1,5) (2,1) (1,11) (6,2) (2,4) (3,7) (5,7) (5,11) (8,5) (6,10) (8,6) (9,7) (7,10) (7,8) (8,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,3]\nnode 1: [4,3]\nnode 2: [5,2]\nnode 3: [3,3]\nnode 4: [1,1]\nnode 5: [9,6]\nnode 6: [3,7]\nnode 7: [3,10]\nnode 8: [6,11]\nnode 9: [3,3]\nnode 10: [7,8]\nnode 11: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph466", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [0,0]\nnode 10: [1,1]\nnode 11: [0,1]\nThe edges are: (9,0) (2,1) (10,1) (9,1) (2,10) (11,2) (2,6) (2,9) (8,3) (9,3) (4,10) (5,7) (5,11) (5,6) (11,6) (9,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,2]\nnode 1: [1,7]\nnode 2: [3,10]\nnode 3: [0,2]\nnode 4: [0,2]\nnode 5: [3,4]\nnode 6: [2,9]\nnode 7: [0,2]\nnode 8: [1,1]\nnode 9: [4,8]\nnode 10: [3,6]\nnode 11: [2,7]." - } - ] - }, - { - "id": "gnn-hard-graph151", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,0]\nnode 8: [0,0]\nnode 9: [1,1]\nThe edges are: (6,0) (9,0) (1,4) (8,1) (2,4) (2,5) (3,4) (6,3) (8,3) (5,4) (7,5) (9,7) (9,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,3]\nnode 1: [6,5]\nnode 2: [4,2]\nnode 3: [7,7]\nnode 4: [2,0]\nnode 5: [4,3]\nnode 6: [3,1]\nnode 7: [1,1]\nnode 8: [1,1]\nnode 9: [6,5]." - } - ] - }, - { - "id": "gnn-hard-graph795", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [0,0]\nnode 10: [0,1]\nnode 11: [0,1]\nnode 12: [1,1]\nnode 13: [1,0]\nnode 14: [1,1]\nThe edges are: (5,0) (10,0) (3,0) (8,0) (12,0) (0,2) (1,13) (6,2) (2,8) (9,2) (2,11) (3,13) (12,3) (13,4) (6,4) (4,9) (4,14) (5,7) (9,5) (5,11) (8,6) (6,12) (7,9) (7,12) (11,7) (13,8) (10,9) (12,10) (13,11) (12,11) (12,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,13]\nnode 1: [2,5]\nnode 2: [12,9]\nnode 3: [6,12]\nnode 4: [6,10]\nnode 5: [9,8]\nnode 6: [6,8]\nnode 7: [9,9]\nnode 8: [6,12]\nnode 9: [5,9]\nnode 10: [6,9]\nnode 11: [6,15]\nnode 12: [14,17]\nnode 13: [13,9]\nnode 14: [2,1]." - } - ] - }, - { - "id": "gnn-hard-graph227", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [1,1]\nThe edges are: (0,7) (0,5) (9,0) (1,8) (5,1) (4,1) (9,1) (8,2) (2,5) (3,6) (4,6) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,4]\nnode 1: [8,6]\nnode 2: [4,4]\nnode 3: [2,2]\nnode 4: [5,6]\nnode 5: [7,8]\nnode 6: [3,1]\nnode 7: [5,4]\nnode 8: [5,7]\nnode 9: [6,6]." - } - ] - }, - { - "id": "gnn-hard-graph209", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [1,0]\nThe edges are: (0,4) (0,6) (0,1) (0,9) (0,8) (5,1) (9,2) (2,8) (3,6) (3,5) (3,9) (8,3) (4,6) (7,4)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [10,4]\nnode 1: [2,4]\nnode 2: [4,2]\nnode 3: [6,4]\nnode 4: [5,5]\nnode 5: [4,1]\nnode 6: [6,5]\nnode 7: [2,1]\nnode 8: [5,5]\nnode 9: [5,5]." - } - ] - }, - { - "id": "gnn-hard-graph457", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [0,1]\nnode 11: [1,1]\nThe edges are: (0,8) (7,1) (2,10) (11,2) (2,3) (2,4) (5,3) (3,8) (3,4) (4,7) (4,6) (10,5) (5,9) (5,6) (8,6) (7,10) (7,8) (10,8) (9,8) (11,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [6,7]\nnode 1: [1,3]\nnode 2: [9,7]\nnode 3: [16,17]\nnode 4: [7,8]\nnode 5: [5,5]\nnode 6: [13,14]\nnode 7: [13,13]\nnode 8: [7,10]\nnode 9: [9,11]\nnode 10: [13,17]\nnode 11: [9,10]." - } - ] - }, - { - "id": "gnn-hard-graph184", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [0,1]\nThe edges are: (8,0) (0,4) (0,7) (6,1) (1,9) (2,1) (2,5) (7,2) (2,9) (4,3) (9,4) (9,5) (9,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [0,2]\nnode 2: [0,4]\nnode 3: [1,1]\nnode 4: [1,4]\nnode 5: [0,2]\nnode 6: [0,1]\nnode 7: [1,4]\nnode 8: [1,2]\nnode 9: [1,5]." - } - ] - }, - { - "id": "gnn-hard-graph504", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [1,1]\nnode 10: [1,0]\nnode 11: [0,0]\nnode 12: [0,1]\nThe edges are: (6,0) (12,0) (9,0) (1,10) (6,2) (3,10) (7,3) (8,3) (3,5) (4,10) (12,4) (8,4) (9,4) (11,5) (5,9) (6,8) (9,6) (11,7) (11,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,8]\nnode 1: [2,1]\nnode 2: [3,3]\nnode 3: [5,4]\nnode 4: [8,8]\nnode 5: [10,5]\nnode 6: [8,9]\nnode 7: [7,2]\nnode 8: [10,7]\nnode 9: [12,11]\nnode 10: [8,4]\nnode 11: [4,4]\nnode 12: [5,6]." - } - ] - }, - { - "id": "gnn-hard-graph236", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [1,1]\nnode 9: [1,0]\nThe edges are: (0,4) (8,0) (1,0) (8,1) (8,2) (7,3) (3,9) (9,4) (8,5) (9,6) (9,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,5]\nnode 1: [5,3]\nnode 2: [3,2]\nnode 3: [3,2]\nnode 4: [4,3]\nnode 5: [3,2]\nnode 6: [2,2]\nnode 7: [1,1]\nnode 8: [7,7]\nnode 9: [6,4]." - } - ] - }, - { - "id": "gnn-hard-graph592", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [1,0]\nnode 12: [1,0]\nThe edges are: (0,10) (0,12) (1,7) (2,9) (2,8) (3,2) (3,5) (3,4) (7,4) (7,5) (6,8) (7,9) (9,11) (10,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,0]\nnode 1: [2,2]\nnode 2: [8,2]\nnode 3: [6,2]\nnode 4: [5,3]\nnode 5: [5,3]\nnode 6: [2,1]\nnode 7: [8,0]\nnode 8: [3,3]\nnode 9: [5,6]\nnode 10: [3,3]\nnode 11: [4,0]\nnode 12: [2,1]." - } - ] - }, - { - "id": "gnn-hard-graph180", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [0,1]\nThe edges are: (2,0) (0,9) (1,4) (2,1) (1,5) (2,5) (4,3) (8,3) (4,6) (7,5) (6,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,1]\nnode 1: [6,3]\nnode 2: [4,5]\nnode 3: [3,2]\nnode 4: [3,4]\nnode 5: [3,4]\nnode 6: [3,2]\nnode 7: [2,1]\nnode 8: [2,2]\nnode 9: [1,2]." - } - ] - }, - { - "id": "gnn-hard-graph122", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [0,0]\nThe edges are: (4,0) (5,0) (1,9) (2,1) (2,8) (5,2) (7,3) (4,6) (5,8) (9,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,2]\nnode 1: [4,1]\nnode 2: [5,3]\nnode 3: [0,1]\nnode 4: [1,2]\nnode 5: [5,2]\nnode 6: [1,1]\nnode 7: [3,2]\nnode 8: [4,1]\nnode 9: [1,2]." - } - ] - }, - { - "id": "gnn-hard-graph296", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [0,0]\nThe edges are: (0,2) (6,0) (6,1) (2,3) (6,2) (4,9) (5,4) (6,8) (7,9) (7,8) (10,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [0,3]\nnode 5: [1,1]\nnode 6: [1,2]\nnode 7: [0,3]\nnode 8: [2,3]\nnode 9: [3,4]\nnode 10: [0,2]." - } - ] - }, - { - "id": "gnn-hard-graph440", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [1,0]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [0,1]\nnode 7: [0,1]\nnode 8: [0,0]\nnode 9: [1,1]\nnode 10: [1,1]\nnode 11: [1,0]\nThe edges are: (0,2) (1,4) (11,1) (2,1) (2,10) (3,9) (10,4) (7,5) (5,10) (6,7) (6,9) (7,9) (8,10) (11,8) (8,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,2]\nnode 1: [6,5]\nnode 2: [1,1]\nnode 3: [1,2]\nnode 4: [1,1]\nnode 5: [1,4]\nnode 6: [2,5]\nnode 7: [3,6]\nnode 8: [2,4]\nnode 9: [6,8]\nnode 10: [9,8]\nnode 11: [4,2]." - } - ] - }, - { - "id": "gnn-hard-graph426", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [0,0]\nnode 8: [1,0]\nnode 9: [1,1]\nnode 10: [0,1]\nnode 11: [0,1]\nThe edges are: (0,7) (4,0) (3,0) (0,9) (0,8) (11,0) (10,1) (1,9) (5,1) (11,1) (8,2) (7,3) (3,6) (9,3) (3,11) (6,7) (9,6) (9,7) (8,7) (7,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [15,13]\nnode 1: [5,7]\nnode 2: [1,1]\nnode 3: [16,14]\nnode 4: [4,3]\nnode 5: [2,4]\nnode 6: [11,10]\nnode 7: [15,14]\nnode 8: [10,7]\nnode 9: [16,16]\nnode 10: [2,4]\nnode 11: [14,14]." - } - ] - }, - { - "id": "gnn-hard-graph653", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [1,0]\nnode 10: [1,0]\nnode 11: [0,1]\nnode 12: [1,0]\nnode 13: [0,1]\nThe edges are: (0,1) (7,0) (1,2) (1,8) (1,7) (2,12) (5,2) (3,10) (3,11) (4,3) (4,8) (4,5) (10,5) (5,6) (5,9) (11,6) (9,7) (13,8) (9,8) (13,11) (12,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,3]\nnode 1: [5,2]\nnode 2: [4,6]\nnode 3: [3,2]\nnode 4: [8,3]\nnode 5: [6,4]\nnode 6: [5,2]\nnode 7: [1,6]\nnode 8: [3,8]\nnode 9: [7,2]\nnode 10: [6,2]\nnode 11: [4,4]\nnode 12: [3,2]\nnode 13: [3,4]." - } - ] - }, - { - "id": "gnn-hard-graph728", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [0,0]\nnode 11: [1,0]\nnode 12: [1,0]\nnode 13: [0,1]\nnode 14: [0,1]\nThe edges are: (2,0) (13,0) (1,2) (1,3) (1,10) (2,13) (11,2) (10,2) (3,8) (4,5) (4,8) (4,10) (10,6) (7,13) (9,14) (9,12) (10,11) (13,11) (14,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,3]\nnode 1: [5,5]\nnode 2: [4,11]\nnode 3: [0,4]\nnode 4: [2,6]\nnode 5: [0,1]\nnode 6: [2,3]\nnode 7: [2,2]\nnode 8: [1,2]\nnode 9: [2,3]\nnode 10: [2,6]\nnode 11: [6,6]\nnode 12: [1,1]\nnode 13: [3,8]\nnode 14: [3,3]." - } - ] - }, - { - "id": "gnn-hard-graph305", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [1,1]\nThe edges are: (0,3) (4,0) (1,4) (8,1) (10,2) (2,4) (5,2) (3,6) (3,5) (9,6) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [1,1]\nnode 2: [3,0]\nnode 3: [2,1]\nnode 4: [5,6]\nnode 5: [4,4]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [1,3]\nnode 9: [0,0]\nnode 10: [3,3]." - } - ] - }, - { - "id": "gnn-hard-graph476", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,0]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [1,1]\nnode 11: [0,0]\nThe edges are: (0,3) (0,5) (1,0) (0,9) (2,1) (1,6) (2,7) (5,3) (3,11) (3,7) (3,6) (8,4) (9,4) (5,10) (8,6) (6,11) (9,6) (11,7) (8,11) (9,8) (11,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [12,5]\nnode 1: [6,6]\nnode 2: [5,1]\nnode 3: [14,9]\nnode 4: [4,4]\nnode 5: [8,3]\nnode 6: [15,9]\nnode 7: [9,5]\nnode 8: [9,10]\nnode 9: [12,12]\nnode 10: [3,1]\nnode 11: [12,8]." - } - ] - }, - { - "id": "gnn-hard-graph615", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [1,1]\nnode 11: [0,0]\nnode 12: [1,0]\nnode 13: [1,1]\nThe edges are: (13,0) (11,0) (7,0) (5,0) (1,10) (9,1) (9,2) (3,2) (3,4) (3,10) (6,3) (4,13) (7,4) (5,4) (5,10) (5,13) (7,10) (8,7) (13,8) (11,8) (9,11) (12,9) (10,12) (12,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [11,11]\nnode 1: [7,5]\nnode 2: [7,5]\nnode 3: [9,6]\nnode 4: [14,12]\nnode 5: [12,12]\nnode 6: [4,3]\nnode 7: [11,11]\nnode 8: [7,8]\nnode 9: [5,5]\nnode 10: [14,12]\nnode 11: [7,7]\nnode 12: [10,8]\nnode 13: [13,13]." - } - ] - }, - { - "id": "gnn-hard-graph123", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [1,1]\nThe edges are: (2,0) (6,0) (0,9) (4,1) (3,1) (5,2) (9,2) (3,6) (3,8) (7,4) (5,7) (9,6) (8,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,6]\nnode 1: [4,4]\nnode 2: [5,7]\nnode 3: [7,2]\nnode 4: [4,1]\nnode 5: [5,3]\nnode 6: [6,9]\nnode 7: [3,2]\nnode 8: [4,6]\nnode 9: [10,7]." - } - ] - }, - { - "id": "gnn-hard-graph527", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [1,1]\nnode 10: [0,0]\nnode 11: [0,1]\nnode 12: [1,0]\nThe edges are: (3,0) (12,1) (8,2) (9,2) (2,6) (5,2) (2,3) (3,12) (3,10) (4,8) (6,4) (4,11) (5,7) (6,9) (12,6) (6,10) (7,10) (11,7) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [2,2]\nnode 2: [9,3]\nnode 3: [10,10]\nnode 4: [4,1]\nnode 5: [4,5]\nnode 6: [13,13]\nnode 7: [4,3]\nnode 8: [6,7]\nnode 9: [10,8]\nnode 10: [7,4]\nnode 11: [2,4]\nnode 12: [6,2]." - } - ] - }, - { - "id": "gnn-hard-graph263", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [1,1]\nThe edges are: (8,0) (1,8) (1,7) (1,3) (6,2) (5,4) (6,5) (6,10) (6,9) (7,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [5,2]\nnode 2: [3,4]\nnode 3: [1,3]\nnode 4: [2,0]\nnode 5: [3,5]\nnode 6: [5,1]\nnode 7: [2,4]\nnode 8: [1,4]\nnode 9: [5,5]\nnode 10: [3,4]." - } - ] - }, - { - "id": "gnn-hard-graph475", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [1,0]\nnode 10: [1,0]\nnode 11: [1,0]\nThe edges are: (0,4) (6,1) (1,2) (2,8) (11,3) (9,4) (6,4) (7,5) (5,10) (6,9) (6,11) (6,10) (9,8) (8,11) (8,10) (10,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,1]\nnode 1: [5,2]\nnode 2: [3,0]\nnode 3: [0,1]\nnode 4: [5,1]\nnode 5: [3,2]\nnode 6: [5,3]\nnode 7: [2,0]\nnode 8: [4,3]\nnode 9: [11,3]\nnode 10: [10,1]\nnode 11: [8,1]." - } - ] - }, - { - "id": "gnn-hard-graph248", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [1,1]\nnode 10: [0,1]\nThe edges are: (0,4) (1,0) (1,10) (1,6) (3,2) (2,10) (9,2) (3,7) (3,6) (5,4) (4,10) (5,10) (10,6) (6,9) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,3]\nnode 1: [3,5]\nnode 2: [1,6]\nnode 3: [5,8]\nnode 4: [1,3]\nnode 5: [2,3]\nnode 6: [1,8]\nnode 7: [0,2]\nnode 8: [1,2]\nnode 9: [4,6]\nnode 10: [5,10]." - } - ] - }, - { - "id": "gnn-hard-graph219", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [0,0]\nnode 8: [1,0]\nnode 9: [1,1]\nThe edges are: (6,0) (8,1) (4,1) (6,1) (1,5) (4,2) (2,5) (2,7) (3,6) (5,9) (6,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [8,5]\nnode 2: [7,5]\nnode 3: [2,2]\nnode 4: [4,3]\nnode 5: [5,4]\nnode 6: [7,6]\nnode 7: [3,3]\nnode 8: [3,2]\nnode 9: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph554", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [1,0]\nnode 10: [0,0]\nnode 11: [0,1]\nnode 12: [1,0]\nThe edges are: (0,11) (0,9) (0,7) (1,3) (8,1) (2,5) (12,2) (8,2) (6,3) (4,3) (10,3) (6,4) (12,5) (12,6) (10,6) (8,7) (8,9) (11,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,4]\nnode 1: [3,5]\nnode 2: [6,6]\nnode 3: [5,1]\nnode 4: [2,3]\nnode 5: [2,3]\nnode 6: [3,4]\nnode 7: [5,5]\nnode 8: [4,4]\nnode 9: [7,6]\nnode 10: [2,3]\nnode 11: [3,4]\nnode 12: [5,3]." - } - ] - }, - { - "id": "gnn-hard-graph719", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [1,0]\nnode 9: [0,0]\nnode 10: [1,0]\nnode 11: [0,1]\nnode 12: [1,1]\nnode 13: [0,1]\nThe edges are: (8,0) (7,0) (2,0) (0,13) (1,8) (6,1) (1,13) (1,11) (2,6) (12,2) (3,5) (4,8) (6,4) (5,4) (6,5) (5,12) (6,10) (9,7) (10,8) (8,12) (8,13) (9,12) (10,11) (12,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,5]\nnode 1: [12,5]\nnode 2: [9,4]\nnode 3: [3,3]\nnode 4: [10,7]\nnode 5: [11,2]\nnode 6: [12,7]\nnode 7: [3,4]\nnode 8: [15,7]\nnode 9: [3,1]\nnode 10: [9,4]\nnode 11: [4,3]\nnode 12: [12,10]\nnode 13: [10,8]." - } - ] - }, - { - "id": "gnn-hard-graph307", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,1]\nnode 10: [0,0]\nThe edges are: (1,0) (10,0) (8,0) (0,5) (9,0) (3,1) (1,10) (8,1) (10,2) (2,5) (2,4) (6,3) (5,3) (3,4) (7,3) (7,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,9]\nnode 1: [3,9]\nnode 2: [2,5]\nnode 3: [2,6]\nnode 4: [1,5]\nnode 5: [1,8]\nnode 6: [1,3]\nnode 7: [2,5]\nnode 8: [1,5]\nnode 9: [0,4]\nnode 10: [1,7]." - } - ] - }, - { - "id": "gnn-hard-graph751", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [1,0]\nnode 10: [1,0]\nnode 11: [0,1]\nnode 12: [0,0]\nnode 13: [0,0]\nnode 14: [1,1]\nThe edges are: (12,0) (10,1) (7,1) (1,3) (14,2) (3,13) (4,3) (13,4) (12,5) (5,11) (5,6) (5,7) (6,14) (14,7) (7,9) (7,13) (7,10) (9,8) (8,10) (9,12) (11,14) (12,14) (12,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,1]\nnode 1: [8,2]\nnode 2: [3,2]\nnode 3: [7,4]\nnode 4: [5,3]\nnode 5: [9,4]\nnode 6: [5,3]\nnode 7: [14,6]\nnode 8: [3,0]\nnode 9: [9,2]\nnode 10: [9,2]\nnode 11: [5,3]\nnode 12: [9,5]\nnode 13: [10,4]\nnode 14: [10,5]." - } - ] - }, - { - "id": "gnn-hard-graph174", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [1,0]\nnode 9: [1,0]\nThe edges are: (0,4) (2,1) (1,6) (8,2) (7,2) (9,2) (7,3) (5,3) (6,4) (5,6) (8,6) (6,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [5,2]\nnode 2: [4,4]\nnode 3: [1,1]\nnode 4: [3,1]\nnode 5: [4,3]\nnode 6: [4,4]\nnode 7: [3,3]\nnode 8: [5,2]\nnode 9: [5,2]." - } - ] - }, - { - "id": "gnn-hard-graph572", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [0,0]\nnode 10: [0,1]\nnode 11: [1,1]\nnode 12: [0,1]\nThe edges are: (0,11) (10,1) (1,8) (1,2) (1,12) (1,9) (2,9) (5,3) (5,4) (4,8) (8,5) (5,6) (7,8) (11,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,0]\nnode 1: [8,6]\nnode 2: [4,4]\nnode 3: [1,3]\nnode 4: [4,5]\nnode 5: [7,6]\nnode 6: [1,3]\nnode 7: [4,2]\nnode 8: [7,10]\nnode 9: [3,4]\nnode 10: [2,3]\nnode 11: [3,3]\nnode 12: [2,3]." - } - ] - }, - { - "id": "gnn-hard-graph132", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [1,0]\nThe edges are: (0,5) (1,9) (3,1) (1,7) (1,8) (9,2) (8,2) (3,4) (7,4) (5,4) (6,5) (9,6) (6,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,2]\nnode 1: [0,4]\nnode 2: [0,2]\nnode 3: [5,3]\nnode 4: [1,4]\nnode 5: [5,1]\nnode 6: [1,4]\nnode 7: [7,3]\nnode 8: [5,3]\nnode 9: [7,3]." - } - ] - }, - { - "id": "gnn-hard-graph665", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [1,1]\nnode 12: [1,0]\nnode 13: [1,0]\nThe edges are: (2,0) (1,9) (1,8) (11,1) (13,2) (2,5) (3,13) (5,3) (4,8) (11,4) (12,4) (8,5) (10,5) (6,9) (12,7) (8,12) (9,10) (9,12) (13,10) (10,12) (13,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,1]\nnode 1: [7,3]\nnode 2: [6,7]\nnode 3: [5,6]\nnode 4: [8,6]\nnode 5: [11,3]\nnode 6: [3,1]\nnode 7: [4,4]\nnode 8: [9,10]\nnode 9: [8,8]\nnode 10: [12,11]\nnode 11: [3,3]\nnode 12: [15,7]\nnode 13: [12,6]." - } - ] - }, - { - "id": "gnn-hard-graph185", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [1,1]\nThe edges are: (2,0) (2,1) (1,5) (3,1) (2,8) (9,2) (2,4) (3,8) (4,6) (5,4) (5,7) (7,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,1]\nnode 1: [6,2]\nnode 2: [0,8]\nnode 3: [0,3]\nnode 4: [6,3]\nnode 5: [0,7]\nnode 6: [0,5]\nnode 7: [3,2]\nnode 8: [4,1]\nnode 9: [3,1]." - } - ] - }, - { - "id": "gnn-hard-graph423", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,1]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [0,1]\nThe edges are: (0,10) (0,1) (8,1) (9,1) (1,2) (2,8) (11,2) (2,6) (3,4) (5,4) (7,5) (11,5) (7,8) (11,8) (10,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,6]\nnode 1: [4,7]\nnode 2: [5,11]\nnode 3: [1,0]\nnode 4: [2,4]\nnode 5: [2,3]\nnode 6: [1,2]\nnode 7: [3,7]\nnode 8: [3,11]\nnode 9: [1,4]\nnode 10: [3,5]\nnode 11: [4,9]." - } - ] - }, - { - "id": "gnn-hard-graph192", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [0,1]\nThe edges are: (0,9) (1,5) (4,1) (1,2) (1,7) (2,5) (9,2) (5,3) (6,4) (8,4) (7,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [3,7]\nnode 2: [4,4]\nnode 3: [1,1]\nnode 4: [2,4]\nnode 5: [4,4]\nnode 6: [1,2]\nnode 7: [3,3]\nnode 8: [1,2]\nnode 9: [1,5]." - } - ] - }, - { - "id": "gnn-hard-graph299", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [0,0]\nThe edges are: (4,0) (9,0) (5,0) (6,0) (7,0) (1,3) (9,1) (7,1) (8,2) (2,7) (4,3) (3,8) (4,10) (6,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [8,5]\nnode 1: [6,2]\nnode 2: [4,1]\nnode 3: [3,2]\nnode 4: [4,1]\nnode 5: [2,1]\nnode 6: [3,1]\nnode 7: [4,2]\nnode 8: [2,0]\nnode 9: [3,2]\nnode 10: [2,2]." - } - ] - }, - { - "id": "gnn-hard-graph496", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [0,0]\nnode 5: [1,1]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [0,0]\nnode 9: [0,0]\nnode 10: [1,0]\nnode 11: [1,0]\nnode 12: [0,1]\nThe edges are: (12,0) (0,4) (9,1) (11,2) (2,4) (3,9) (3,11) (6,3) (3,5) (6,4) (11,6) (8,6) (9,7) (7,8) (8,9) (8,12) (10,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,2]\nnode 1: [1,2]\nnode 2: [5,5]\nnode 3: [4,7]\nnode 4: [2,2]\nnode 5: [3,2]\nnode 6: [9,10]\nnode 7: [2,5]\nnode 8: [4,3]\nnode 9: [4,5]\nnode 10: [2,0]\nnode 11: [5,3]\nnode 12: [1,5]." - } - ] - }, - { - "id": "gnn-hard-graph62", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [1,1]\nThe edges are: (0,2) (1,7) (4,1) (3,2) (5,3) (7,4) (4,5) (6,4) (8,5) (8,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,1]\nnode 1: [4,4]\nnode 2: [2,1]\nnode 3: [1,2]\nnode 4: [4,3]\nnode 5: [4,4]\nnode 6: [2,2]\nnode 7: [4,3]\nnode 8: [3,3]." - } - ] - }, - { - "id": "gnn-hard-graph14", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [0,0]\nThe edges are: (7,0) (0,3) (4,1) (8,1) (5,1) (4,2) (6,2) (7,3) (3,5) (4,5) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,1]\nnode 1: [3,4]\nnode 2: [3,1]\nnode 3: [4,4]\nnode 4: [2,3]\nnode 5: [5,1]\nnode 6: [0,1]\nnode 7: [3,2]\nnode 8: [3,1]." - } - ] - }, - { - "id": "gnn-hard-graph395", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [1,0]\nnode 11: [0,1]\nThe edges are: (3,0) (9,0) (4,1) (6,1) (2,5) (8,2) (3,11) (5,4) (9,6) (11,6) (11,7) (7,8) (9,8) (10,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,3]\nnode 1: [0,3]\nnode 2: [3,5]\nnode 3: [2,4]\nnode 4: [3,3]\nnode 5: [0,2]\nnode 6: [3,4]\nnode 7: [2,5]\nnode 8: [1,3]\nnode 9: [2,8]\nnode 10: [1,1]\nnode 11: [0,5]." - } - ] - }, - { - "id": "gnn-hard-graph74", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [0,1]\nThe edges are: (0,6) (7,1) (4,2) (6,2) (8,2) (5,3) (5,8) (7,6) (8,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,2]\nnode 1: [1,1]\nnode 2: [5,4]\nnode 3: [1,2]\nnode 4: [2,2]\nnode 5: [2,1]\nnode 6: [4,3]\nnode 7: [5,3]\nnode 8: [4,5]." - } - ] - }, - { - "id": "gnn-hard-graph280", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [0,0]\nnode 10: [0,1]\nThe edges are: (1,0) (6,0) (9,0) (4,0) (7,1) (10,1) (4,1) (2,6) (3,8) (10,3) (8,4) (7,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,4]\nnode 1: [7,7]\nnode 2: [1,0]\nnode 3: [1,4]\nnode 4: [3,8]\nnode 5: [2,1]\nnode 6: [1,4]\nnode 7: [3,4]\nnode 8: [4,2]\nnode 9: [1,3]\nnode 10: [3,4]." - } - ] - }, - { - "id": "gnn-hard-graph693", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [0,0]\nnode 10: [1,0]\nnode 11: [1,0]\nnode 12: [0,0]\nnode 13: [1,0]\nThe edges are: (11,0) (13,1) (1,4) (1,5) (2,13) (2,9) (6,2) (4,2) (8,2) (6,3) (3,4) (3,12) (6,4) (4,10) (5,10) (6,13) (7,6) (10,9) (12,11) (12,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,0]\nnode 1: [4,1]\nnode 2: [10,3]\nnode 3: [8,4]\nnode 4: [10,3]\nnode 5: [3,0]\nnode 6: [6,2]\nnode 7: [4,2]\nnode 8: [2,1]\nnode 9: [3,1]\nnode 10: [5,1]\nnode 11: [3,1]\nnode 12: [3,0]\nnode 13: [10,4]." - } - ] - }, - { - "id": "gnn-hard-graph337", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [0,0]\nnode 9: [0,0]\nnode 10: [1,1]\nThe edges are: (0,6) (1,0) (1,2) (1,10) (1,9) (4,2) (2,5) (7,2) (3,2) (4,10) (8,5) (10,6) (10,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,5]\nnode 1: [3,8]\nnode 2: [7,8]\nnode 3: [1,4]\nnode 4: [2,6]\nnode 5: [2,5]\nnode 6: [2,3]\nnode 7: [1,4]\nnode 8: [2,3]\nnode 9: [2,3]\nnode 10: [6,8]." - } - ] - }, - { - "id": "gnn-hard-graph382", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,0]\nnode 5: [0,1]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [1,0]\nnode 9: [0,0]\nnode 10: [1,1]\nnode 11: [1,0]\nThe edges are: (0,9) (0,4) (7,0) (0,11) (1,4) (4,2) (2,11) (7,3) (8,4) (4,10) (6,4) (10,5) (8,7) (9,8) (11,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [11,1]\nnode 1: [5,1]\nnode 2: [6,1]\nnode 3: [2,0]\nnode 4: [10,3]\nnode 5: [1,1]\nnode 6: [5,1]\nnode 7: [6,3]\nnode 8: [10,1]\nnode 9: [6,2]\nnode 10: [6,2]\nnode 11: [8,1]." - } - ] - }, - { - "id": "gnn-hard-graph372", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [0,0]\nnode 8: [0,0]\nnode 9: [1,1]\nnode 10: [0,1]\nnode 11: [1,1]\nThe edges are: (9,0) (3,0) (0,11) (7,0) (8,1) (11,1) (1,10) (2,6) (6,3) (6,4) (7,4) (5,8) (9,6) (7,8) (10,8) (9,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,5]\nnode 1: [2,2]\nnode 2: [3,3]\nnode 3: [5,6]\nnode 4: [4,4]\nnode 5: [1,1]\nnode 6: [1,5]\nnode 7: [3,5]\nnode 8: [2,3]\nnode 9: [6,7]\nnode 10: [2,3]\nnode 11: [4,7]." - } - ] - }, - { - "id": "gnn-hard-graph141", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [1,0]\nnode 9: [1,1]\nThe edges are: (0,2) (0,5) (1,4) (3,2) (2,6) (8,3) (3,7) (8,4) (5,9) (8,7) (9,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [5,1]\nnode 1: [1,0]\nnode 2: [2,3]\nnode 3: [8,2]\nnode 4: [3,3]\nnode 5: [1,1]\nnode 6: [3,0]\nnode 7: [5,3]\nnode 8: [6,1]\nnode 9: [5,3]." - } - ] - }, - { - "id": "gnn-hard-graph218", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [1,0]\nnode 4: [0,1]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [1,0]\nnode 9: [1,0]\nThe edges are: (5,0) (0,4) (2,1) (6,1) (1,4) (6,3) (8,3) (3,9) (4,3) (7,6) (6,9) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,1]\nnode 1: [4,3]\nnode 2: [1,2]\nnode 3: [8,2]\nnode 4: [5,4]\nnode 5: [1,1]\nnode 6: [8,3]\nnode 7: [5,1]\nnode 8: [5,1]\nnode 9: [6,2]." - } - ] - }, - { - "id": "gnn-hard-graph767", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [1,1]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [0,1]\nnode 10: [1,0]\nnode 11: [1,0]\nnode 12: [1,0]\nnode 13: [1,0]\nnode 14: [1,0]\nThe edges are: (7,0) (13,0) (1,8) (1,10) (11,1) (12,1) (14,2) (2,4) (2,9) (10,2) (12,2) (2,3) (3,14) (5,3) (3,11) (12,3) (4,5) (6,4) (11,4) (7,5) (5,8) (5,12) (13,6) (6,11) (7,13) (9,7) (9,10) (12,10) (13,11)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,3]\nnode 1: [11,11]\nnode 2: [15,9]\nnode 3: [15,14]\nnode 4: [12,11]\nnode 5: [14,10]\nnode 6: [7,7]\nnode 7: [9,4]\nnode 8: [6,4]\nnode 9: [8,7]\nnode 10: [13,7]\nnode 11: [13,6]\nnode 12: [16,10]\nnode 13: [9,7]\nnode 14: [8,4]." - } - ] - }, - { - "id": "gnn-hard-graph651", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [0,0]\nnode 12: [1,0]\nnode 13: [0,0]\nThe edges are: (0,1) (0,6) (11,2) (2,12) (10,3) (9,3) (6,3) (4,5) (5,7) (10,5) (5,9) (8,5) (8,7) (8,12) (9,10) (11,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [2,0]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [2,2]\nnode 4: [2,3]\nnode 5: [3,3]\nnode 6: [1,3]\nnode 7: [3,3]\nnode 8: [4,5]\nnode 9: [3,6]\nnode 10: [4,6]\nnode 11: [1,0]\nnode 12: [2,0]\nnode 13: [0,0]." - } - ] - }, - { - "id": "gnn-hard-graph70", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [1,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,0]\nnode 7: [0,1]\nnode 8: [0,0]\nThe edges are: (0,6) (8,0) (0,4) (5,1) (8,1) (2,6) (4,2) (7,3) (4,6) (4,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,6]\nnode 1: [2,1]\nnode 2: [2,5]\nnode 3: [1,1]\nnode 4: [6,3]\nnode 5: [0,0]\nnode 6: [5,3]\nnode 7: [1,4]\nnode 8: [2,0]." - } - ] - }, - { - "id": "gnn-hard-graph721", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [1,1]\nnode 3: [1,0]\nnode 4: [1,0]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [1,0]\nnode 10: [0,1]\nnode 11: [0,0]\nnode 12: [0,1]\nnode 13: [1,1]\nnode 14: [0,1]\nThe edges are: (0,6) (0,5) (12,0) (0,7) (1,6) (1,11) (3,1) (2,1) (2,8) (2,10) (3,5) (11,3) (3,12) (4,7) (14,5) (6,9) (6,12) (10,6) (7,13) (7,12) (13,8) (9,13) (10,14) (12,13)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,13]\nnode 1: [2,10]\nnode 2: [7,7]\nnode 3: [8,9]\nnode 4: [2,3]\nnode 5: [1,6]\nnode 6: [11,14]\nnode 7: [5,11]\nnode 8: [1,6]\nnode 9: [2,7]\nnode 10: [1,8]\nnode 11: [3,4]\nnode 12: [5,15]\nnode 13: [9,11]\nnode 14: [3,5]." - } - ] - }, - { - "id": "gnn-hard-graph109", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [1,1]\nnode 5: [0,1]\nnode 6: [1,1]\nnode 7: [1,1]\nnode 8: [0,0]\nThe edges are: (0,3) (8,0) (0,4) (6,1) (7,2) (3,2) (4,3) (7,5) (7,6) (8,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [7,6]\nnode 1: [1,2]\nnode 2: [5,4]\nnode 3: [6,6]\nnode 4: [5,4]\nnode 5: [2,2]\nnode 6: [3,3]\nnode 7: [6,7]\nnode 8: [4,4]." - } - ] - }, - { - "id": "gnn-hard-graph553", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [1,1]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [0,0]\nnode 12: [0,0]\nThe edges are: (0,2) (1,10) (2,9) (2,12) (2,7) (6,2) (9,3) (8,3) (10,4) (4,8) (7,4) (4,6) (5,9) (8,6) (7,6) (7,11) (7,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,4]\nnode 1: [1,3]\nnode 2: [5,11]\nnode 3: [2,3]\nnode 4: [8,13]\nnode 5: [0,1]\nnode 6: [9,14]\nnode 7: [7,16]\nnode 8: [6,10]\nnode 9: [2,7]\nnode 10: [7,9]\nnode 11: [3,4]\nnode 12: [1,4]." - } - ] - }, - { - "id": "gnn-hard-graph484", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,0]\nnode 2: [1,1]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [0,1]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [1,1]\nnode 10: [1,0]\nnode 11: [1,0]\nnode 12: [0,0]\nThe edges are: (0,3) (1,0) (0,11) (10,0) (0,9) (1,8) (5,1) (2,11) (2,6) (7,3) (9,3) (11,4) (4,12) (6,4) (5,7) (5,11) (12,5) (7,6) (10,6) (6,9) (8,11) (8,10) (11,10) (12,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [15,7]\nnode 1: [7,1]\nnode 2: [9,4]\nnode 3: [5,3]\nnode 4: [11,4]\nnode 5: [11,4]\nnode 6: [7,6]\nnode 7: [9,3]\nnode 8: [11,5]\nnode 9: [10,4]\nnode 10: [16,5]\nnode 11: [12,5]\nnode 12: [6,3]." - } - ] - }, - { - "id": "gnn-hard-graph762", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,0]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [1,1]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [0,1]\nnode 9: [1,0]\nnode 10: [1,1]\nnode 11: [0,1]\nnode 12: [0,0]\nnode 13: [0,1]\nnode 14: [1,1]\nThe edges are: (0,13) (0,2) (6,0) (12,1) (1,2) (3,2) (5,2) (6,3) (14,4) (4,11) (10,5) (9,5) (13,7) (7,11) (10,8) (8,12) (9,13) (10,12)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,6]\nnode 1: [2,5]\nnode 2: [6,2]\nnode 3: [2,5]\nnode 4: [2,2]\nnode 5: [1,7]\nnode 6: [2,1]\nnode 7: [3,2]\nnode 8: [1,4]\nnode 9: [5,2]\nnode 10: [5,4]\nnode 11: [1,4]\nnode 12: [2,3]\nnode 13: [1,5]\nnode 14: [1,2]." - } - ] - }, - { - "id": "gnn-hard-graph557", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,1]\nnode 2: [0,1]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [1,0]\nnode 7: [1,0]\nnode 8: [1,1]\nnode 9: [1,0]\nnode 10: [1,1]\nnode 11: [0,0]\nnode 12: [1,1]\nThe edges are: (7,0) (8,0) (1,12) (5,1) (7,2) (2,10) (2,9) (2,4) (3,9) (4,12) (4,5) (11,5) (6,5) (7,12) (11,8) (9,10)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [3,2]\nnode 1: [4,2]\nnode 2: [7,8]\nnode 3: [2,3]\nnode 4: [7,3]\nnode 5: [7,4]\nnode 6: [2,1]\nnode 7: [7,3]\nnode 8: [4,2]\nnode 9: [5,2]\nnode 10: [5,4]\nnode 11: [3,1]\nnode 12: [6,5]." - } - ] - }, - { - "id": "gnn-hard-graph71", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [0,1]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [1,0]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,1]\nThe edges are: (0,2) (0,1) (2,1) (5,1) (2,3) (2,4) (3,7) (3,6) (4,3) (7,4) (4,6) (8,6)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,3]\nnode 1: [2,5]\nnode 2: [3,8]\nnode 3: [4,8]\nnode 4: [5,7]\nnode 5: [2,1]\nnode 6: [1,5]\nnode 7: [1,5]\nnode 8: [1,2]." - } - ] - }, - { - "id": "gnn-hard-graph789", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,1]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [0,0]\nnode 5: [1,0]\nnode 6: [0,0]\nnode 7: [0,0]\nnode 8: [1,1]\nnode 9: [1,1]\nnode 10: [0,0]\nnode 11: [1,0]\nnode 12: [0,1]\nnode 13: [1,0]\nnode 14: [1,0]\nThe edges are: (7,0) (0,1) (3,0) (8,0) (11,1) (14,1) (2,4) (8,2) (13,3) (3,14) (6,3) (11,4) (4,12) (5,13) (7,5) (9,6) (7,10) (14,8) (9,11) (11,10) (10,12) (13,11) (13,14)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [6,4]\nnode 1: [5,6]\nnode 2: [2,2]\nnode 3: [7,5]\nnode 4: [3,3]\nnode 5: [4,1]\nnode 6: [3,1]\nnode 7: [3,3]\nnode 8: [4,5]\nnode 9: [3,3]\nnode 10: [3,3]\nnode 11: [8,3]\nnode 12: [2,2]\nnode 13: [7,5]\nnode 14: [8,3]." - } - ] - }, - { - "id": "gnn-hard-graph491", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,0]\nnode 1: [1,0]\nnode 2: [1,0]\nnode 3: [1,1]\nnode 4: [0,0]\nnode 5: [0,0]\nnode 6: [1,1]\nnode 7: [0,1]\nnode 8: [0,0]\nnode 9: [0,1]\nnode 10: [1,1]\nnode 11: [1,0]\nnode 12: [1,1]\nThe edges are: (0,7) (0,8) (10,0) (6,1) (5,1) (12,2) (7,3) (6,4) (5,12) (11,6) (7,9) (11,7) (8,11) (11,9)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [6,2]\nnode 1: [4,1]\nnode 2: [1,0]\nnode 3: [3,2]\nnode 4: [2,0]\nnode 5: [2,1]\nnode 6: [3,5]\nnode 7: [3,7]\nnode 8: [2,5]\nnode 9: [4,5]\nnode 10: [1,2]\nnode 11: [8,3]\nnode 12: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph210", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [1,1]\nnode 1: [0,1]\nnode 2: [1,0]\nnode 3: [0,0]\nnode 4: [0,1]\nnode 5: [1,1]\nnode 6: [0,0]\nnode 7: [1,1]\nnode 8: [0,1]\nnode 9: [1,1]\nThe edges are: (0,9) (0,7) (1,6) (1,2) (2,7) (3,8) (4,3) (5,7) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [4,4]\nnode 1: [1,3]\nnode 2: [4,3]\nnode 3: [1,1]\nnode 4: [0,2]\nnode 5: [3,3]\nnode 6: [1,0]\nnode 7: [5,6]\nnode 8: [3,5]\nnode 9: [2,2]." - } - ] - }, - { - "id": "gnn-hard-graph128", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,1]\nnode 1: [0,0]\nnode 2: [0,1]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,1]\nnode 6: [0,0]\nnode 7: [1,0]\nnode 8: [0,1]\nnode 9: [1,0]\nThe edges are: (9,0) (0,7) (3,0) (0,6) (1,7) (4,2) (3,5) (4,9) (6,8) (7,8)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,8]\nnode 1: [0,2]\nnode 2: [1,1]\nnode 3: [2,2]\nnode 4: [0,3]\nnode 5: [0,2]\nnode 6: [3,1]\nnode 7: [4,1]\nnode 8: [0,4]\nnode 9: [3,2]." - } - ] - }, - { - "id": "gnn-hard-graph57", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [0,0]\nnode 3: [0,0]\nnode 4: [1,1]\nnode 5: [0,1]\nnode 6: [1,0]\nnode 7: [1,1]\nnode 8: [1,0]\nThe edges are: (1,0) (8,0) (2,7) (3,8) (6,4) (4,7) (4,5) (8,5)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [0,1]\nnode 1: [2,1]\nnode 2: [1,1]\nnode 3: [0,1]\nnode 4: [4,3]\nnode 5: [2,3]\nnode 6: [2,2]\nnode 7: [3,3]\nnode 8: [5,2]." - } - ] - }, - { - "id": "gnn-hard-graph238", - "conversations": [ - { - "from": "human", - "value": "In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.\nEmbeddings:\nnode 0: [0,0]\nnode 1: [1,1]\nnode 2: [1,0]\nnode 3: [0,1]\nnode 4: [0,1]\nnode 5: [0,0]\nnode 6: [0,0]\nnode 7: [0,1]\nnode 8: [0,1]\nnode 9: [1,0]\nThe edges are: (3,0) (1,2) (1,8) (2,3) (3,5) (4,7) (6,9) (6,7) (8,7)\nIn a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.\nQ: What's the embedding of each node after one layer of simple graph convolution layer?" - }, - { - "from": "gpt", - "value": "The updated embeddings of each node:\nnode 0: [1,0]\nnode 1: [2,4]\nnode 2: [2,1]\nnode 3: [1,4]\nnode 4: [0,2]\nnode 5: [1,0]\nnode 6: [0,2]\nnode 7: [2,4]\nnode 8: [1,3]\nnode 9: [1,1]." - } - ] - } -] \ No newline at end of file +version https://git-lfs.github.com/spec/v1 +oid sha256:d1363bacdea65933860f2a83248068e40501a12d63d0ccdc84ba15ff5c5d6a81 +size 348984