174 lines
5.7 KiB
Python
174 lines
5.7 KiB
Python
"""
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===========================
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Depth First Search on Edges
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===========================
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Algorithms for a depth-first traversal of edges in a graph.
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"""
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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_dfs"]
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def edge_dfs(G, source=None, orientation=None):
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"""A directed, depth-first-search of edges in `G`, beginning at `source`.
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Yield the edges of G in a depth-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 depth-first traversal.
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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, 1), (3, 1)]
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>>> list(nx.edge_dfs(nx.Graph(edges), nodes))
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[(0, 1), (1, 2), (1, 3)]
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>>> list(nx.edge_dfs(nx.DiGraph(edges), nodes))
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[(0, 1), (1, 0), (2, 1), (3, 1)]
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>>> list(nx.edge_dfs(nx.MultiGraph(edges), nodes))
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[(0, 1, 0), (1, 0, 1), (0, 1, 2), (1, 2, 0), (1, 3, 0)]
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>>> list(nx.edge_dfs(nx.MultiDiGraph(edges), nodes))
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[(0, 1, 0), (1, 0, 0), (1, 0, 1), (2, 1, 0), (3, 1, 0)]
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>>> list(nx.edge_dfs(nx.DiGraph(edges), nodes, orientation="ignore"))
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[(0, 1, 'forward'), (1, 0, 'forward'), (2, 1, 'reverse'), (3, 1, 'reverse')]
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>>> list(nx.edge_dfs(nx.MultiDiGraph(edges), nodes, orientation="ignore"))
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[(0, 1, 0, 'forward'), (1, 0, 0, 'forward'), (1, 0, 1, '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 depth-first traversal of nodes, as provided by
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:func:`networkx.algorithms.traversal.depth_first_search.dfs_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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See Also
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--------
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dfs_edges
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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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# set up formation of edge_id to easily look up if edge already returned
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if directed:
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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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def edge_id(edge):
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# single id for undirected requires frozenset on nodes
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return (frozenset(edge[:2]),) + edge[2:]
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# Basic setup
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check_reverse = directed and orientation in ("reverse", "ignore")
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visited_edges = set()
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visited_nodes = set()
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edges = {}
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# start DFS
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for start_node in nodes:
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stack = [start_node]
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while stack:
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current_node = stack[-1]
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if current_node not in visited_nodes:
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edges[current_node] = edges_from(current_node)
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visited_nodes.add(current_node)
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try:
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edge = next(edges[current_node])
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except StopIteration:
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# No more edges from the current node.
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stack.pop()
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else:
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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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# Mark the traversed "to" node as to-be-explored.
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if check_reverse and edge[-1] == REVERSE:
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stack.append(edge[0])
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else:
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stack.append(edge[1])
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yield edge
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