| """ |
| ============================= |
| Breadth First Search on Edges |
| ============================= |
| |
| Algorithms for a breadth-first traversal of edges in a graph. |
| |
| """ |
|
|
| from collections import deque |
|
|
| import networkx as nx |
|
|
| FORWARD = "forward" |
| REVERSE = "reverse" |
|
|
| __all__ = ["edge_bfs"] |
|
|
|
|
| @nx._dispatchable |
| def edge_bfs(G, source=None, orientation=None): |
| """A directed, breadth-first-search of edges in `G`, beginning at `source`. |
| |
| Yield the edges of G in a breadth-first-search order continuing until |
| all edges are generated. |
| |
| Parameters |
| ---------- |
| G : graph |
| A directed/undirected graph/multigraph. |
| |
| source : node, list of nodes |
| The node from which the traversal begins. If None, then a source |
| is chosen arbitrarily and repeatedly until all edges from each node in |
| the graph are searched. |
| |
| orientation : None | 'original' | 'reverse' | 'ignore' (default: None) |
| For directed graphs and directed multigraphs, edge traversals need not |
| respect the original orientation of the edges. |
| When set to 'reverse' every edge is traversed in the reverse direction. |
| When set to 'ignore', every edge is treated as undirected. |
| When set to 'original', every edge is treated as directed. |
| In all three cases, the yielded edge tuples add a last entry to |
| indicate the direction in which that edge was traversed. |
| If orientation is None, the yielded edge has no direction indicated. |
| The direction is respected, but not reported. |
| |
| Yields |
| ------ |
| edge : directed edge |
| A directed edge indicating the path taken by the breadth-first-search. |
| For graphs, `edge` is of the form `(u, v)` where `u` and `v` |
| are the tail and head of the edge as determined by the traversal. |
| For multigraphs, `edge` is of the form `(u, v, key)`, where `key` is |
| the key of the edge. When the graph is directed, then `u` and `v` |
| are always in the order of the actual directed edge. |
| If orientation is not None then the edge tuple is extended to include |
| the direction of traversal ('forward' or 'reverse') on that edge. |
| |
| Examples |
| -------- |
| >>> nodes = [0, 1, 2, 3] |
| >>> edges = [(0, 1), (1, 0), (1, 0), (2, 0), (2, 1), (3, 1)] |
| |
| >>> list(nx.edge_bfs(nx.Graph(edges), nodes)) |
| [(0, 1), (0, 2), (1, 2), (1, 3)] |
| |
| >>> list(nx.edge_bfs(nx.DiGraph(edges), nodes)) |
| [(0, 1), (1, 0), (2, 0), (2, 1), (3, 1)] |
| |
| >>> list(nx.edge_bfs(nx.MultiGraph(edges), nodes)) |
| [(0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 2, 0), (1, 2, 0), (1, 3, 0)] |
| |
| >>> list(nx.edge_bfs(nx.MultiDiGraph(edges), nodes)) |
| [(0, 1, 0), (1, 0, 0), (1, 0, 1), (2, 0, 0), (2, 1, 0), (3, 1, 0)] |
| |
| >>> list(nx.edge_bfs(nx.DiGraph(edges), nodes, orientation="ignore")) |
| [(0, 1, 'forward'), (1, 0, 'reverse'), (2, 0, 'reverse'), (2, 1, 'reverse'), (3, 1, 'reverse')] |
| |
| >>> list(nx.edge_bfs(nx.MultiDiGraph(edges), nodes, orientation="ignore")) |
| [(0, 1, 0, 'forward'), (1, 0, 0, 'reverse'), (1, 0, 1, 'reverse'), (2, 0, 0, 'reverse'), (2, 1, 0, 'reverse'), (3, 1, 0, 'reverse')] |
| |
| Notes |
| ----- |
| The goal of this function is to visit edges. It differs from the more |
| familiar breadth-first-search of nodes, as provided by |
| :func:`networkx.algorithms.traversal.breadth_first_search.bfs_edges`, in |
| that it does not stop once every node has been visited. In a directed graph |
| with edges [(0, 1), (1, 2), (2, 1)], the edge (2, 1) would not be visited |
| if not for the functionality provided by this function. |
| |
| The naming of this function is very similar to bfs_edges. The difference |
| is that 'edge_bfs' yields edges even if they extend back to an already |
| explored node while 'bfs_edges' yields the edges of the tree that results |
| from a breadth-first-search (BFS) so no edges are reported if they extend |
| to already explored nodes. That means 'edge_bfs' reports all edges while |
| 'bfs_edges' only report those traversed by a node-based BFS. Yet another |
| description is that 'bfs_edges' reports the edges traversed during BFS |
| while 'edge_bfs' reports all edges in the order they are explored. |
| |
| See Also |
| -------- |
| bfs_edges |
| bfs_tree |
| edge_dfs |
| |
| """ |
| nodes = list(G.nbunch_iter(source)) |
| if not nodes: |
| return |
|
|
| directed = G.is_directed() |
| kwds = {"data": False} |
| if G.is_multigraph() is True: |
| kwds["keys"] = True |
|
|
| |
| if orientation is None: |
|
|
| def edges_from(node): |
| return iter(G.edges(node, **kwds)) |
|
|
| elif not directed or orientation == "original": |
|
|
| def edges_from(node): |
| for e in G.edges(node, **kwds): |
| yield e + (FORWARD,) |
|
|
| elif orientation == "reverse": |
|
|
| def edges_from(node): |
| for e in G.in_edges(node, **kwds): |
| yield e + (REVERSE,) |
|
|
| elif orientation == "ignore": |
|
|
| def edges_from(node): |
| for e in G.edges(node, **kwds): |
| yield e + (FORWARD,) |
| for e in G.in_edges(node, **kwds): |
| yield e + (REVERSE,) |
|
|
| else: |
| raise nx.NetworkXError("invalid orientation argument.") |
|
|
| if directed: |
| neighbors = G.successors |
|
|
| def edge_id(edge): |
| |
| return edge[:-1] if orientation is not None else edge |
|
|
| else: |
| neighbors = G.neighbors |
|
|
| def edge_id(edge): |
| return (frozenset(edge[:2]),) + edge[2:] |
|
|
| check_reverse = directed and orientation in ("reverse", "ignore") |
|
|
| |
| visited_nodes = set(nodes) |
| visited_edges = set() |
| queue = deque([(n, edges_from(n)) for n in nodes]) |
| while queue: |
| parent, children_edges = queue.popleft() |
| for edge in children_edges: |
| if check_reverse and edge[-1] == REVERSE: |
| child = edge[0] |
| else: |
| child = edge[1] |
| if child not in visited_nodes: |
| visited_nodes.add(child) |
| queue.append((child, edges_from(child))) |
| edgeid = edge_id(edge) |
| if edgeid not in visited_edges: |
| visited_edges.add(edgeid) |
| yield edge |
|
|
