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