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| """ | |
| ============================= | |
| 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"] | |
| 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 | |
| # set up edge lookup | |
| 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): | |
| # remove direction indicator | |
| 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") | |
| # start BFS | |
| 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 | |