File size: 5,139 Bytes
1c8033c | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 | """Graph utilities for bipartite user-item graphs."""
import numpy as np
from collections import defaultdict, deque
from typing import List, Tuple, Set, Dict, Optional
def build_adjacency(edges, N, M):
"""Build adjacency lists for bipartite graph.
Returns:
user_to_items: dict[int, list[int]]
item_to_users: dict[int, list[int]]
edge_dict: dict[(i,j), x_ij]
"""
user_to_items = defaultdict(list)
item_to_users = defaultdict(list)
edge_dict = {}
for e in edges:
i, j = int(e[0]), int(e[1])
x = e[2] if len(e) > 2 else 1
user_to_items[i].append(j)
item_to_users[j].append(i)
edge_dict[(i, j)] = x
return dict(user_to_items), dict(item_to_users), edge_dict
def bfs_neighborhood(seed_nodes, adj_func, N, M, radius, user_to_items, item_to_users):
"""BFS on bipartite graph from seed set.
Returns dict mapping node_id -> distance from seed set.
Users: 0..N-1, Items: N..N+M-1
"""
distances = {}
queue = deque()
for node in seed_nodes:
distances[node] = 0
queue.append((node, 0))
while queue:
node, dist = queue.popleft()
if dist >= radius:
continue
if node < N: # User node
neighbors = [j + N for j in user_to_items.get(node, [])]
else: # Item node
j = node - N
neighbors = list(item_to_users.get(j, []))
for nbr in neighbors:
if nbr not in distances:
distances[nbr] = dist + 1
queue.append((nbr, dist + 1))
return distances
def get_deletion_neighborhood(edge_to_remove, user_to_items, item_to_users,
N, M, radius):
"""Get neighborhood of deletion edge (i, j, x)."""
i = int(edge_to_remove[0])
j = int(edge_to_remove[1])
seed_nodes = {i, j + N}
return bfs_neighborhood(seed_nodes, None, N, M, radius, user_to_items, item_to_users)
def get_blocks_at_distance(distances, N):
"""Group blocks by distance."""
by_distance = defaultdict(list)
for node, dist in distances.items():
if node < N:
by_distance[dist].append(('user', node))
else:
by_distance[dist].append(('item', node - N))
return dict(by_distance)
def get_user_item_sets_in_radius(distances, N, radius):
"""Get sets of user and item indices within radius R."""
users_in_R = set()
items_in_R = set()
for node, dist in distances.items():
if dist <= radius:
if node < N:
users_in_R.add(node)
else:
items_in_R.add(node - N)
return users_in_R, items_in_R
def generate_bounded_degree_graph(N, M, avg_degree, seed=0):
"""Generate bipartite graph where each user has ~avg_degree items."""
rng = np.random.RandomState(seed)
edges_set = set()
for i in range(N):
deg = max(1, rng.poisson(avg_degree))
deg = min(deg, M, 2 * avg_degree)
items = rng.choice(M, size=deg, replace=False)
for j in items:
edges_set.add((i, int(j)))
return list(edges_set)
def generate_erdos_renyi_graph(N, M, avg_degree, seed=0):
"""Generate Erdos-Renyi bipartite graph."""
rng = np.random.RandomState(seed)
p = avg_degree / M
p = min(p, 1.0)
edges_set = set()
for i in range(N):
mask = rng.random(M) < p
for j in np.where(mask)[0]:
edges_set.add((i, int(j)))
for i in range(N):
if not any(e[0] == i for e in edges_set):
j = rng.randint(M)
edges_set.add((i, j))
return list(edges_set)
def generate_power_law_graph(N, M, avg_degree, seed=0, alpha=2.5):
"""Generate bipartite graph with power-law degree distribution."""
rng = np.random.RandomState(seed)
edges_set = set()
item_weights = np.arange(1, M + 1, dtype=float) ** (-alpha + 1)
item_weights /= item_weights.sum()
for i in range(N):
deg = max(1, int(rng.pareto(alpha - 1) * avg_degree / max(alpha - 2, 0.5) + 1))
deg = min(deg, M)
items = rng.choice(M, size=deg, replace=False, p=item_weights)
for j in items:
edges_set.add((i, int(j)))
return list(edges_set)
def compute_graph_stats(edges, N, M):
"""Compute graph statistics."""
user_degrees = defaultdict(int)
item_degrees = defaultdict(int)
for e in edges:
user_degrees[e[0]] += 1
item_degrees[e[1]] += 1
udeg = list(user_degrees.values()) if user_degrees else [0]
ideg = list(item_degrees.values()) if item_degrees else [0]
return {
'n_edges': len(edges),
'n_users_active': len(user_degrees),
'n_items_active': len(item_degrees),
'user_degree_mean': float(np.mean(udeg)),
'user_degree_max': int(np.max(udeg)),
'user_degree_min': int(np.min(udeg)),
'item_degree_mean': float(np.mean(ideg)),
'item_degree_max': int(np.max(ideg)),
'item_degree_min': int(np.min(ideg)),
}
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