NetworkX

Source code for networkx.algorithms.simple_paths

# -*- coding: utf-8 -*-
#    Copyright (C) 2012 by
#    Sergio Nery Simoes <sergionery@gmail.com>
#    All rights reserved.
#    BSD license.
import networkx as nx
__author__ = """\n""".join(['Sérgio Nery Simões <sergionery@gmail.com>',
                            'Aric Hagberg <aric.hagberg@gmail.com>'])
__all__ = ['all_simple_paths']

[docs]def all_simple_paths(G, source, target, cutoff=None): """Generate all simple paths in the graph G from source to target. A simple path is a path with no repeated nodes. Parameters ---------- G : NetworkX graph source : node Starting node for path target : node Ending node for path cutoff : integer, optional Depth to stop the search. Only paths of length <= cutoff are returned. Returns ------- path_generator: generator A generator that produces lists of simple paths. If there are no paths between the source and target within the given cutoff the generator produces no output. Examples -------- >>> G = nx.complete_graph(4) >>> for path in nx.all_simple_paths(G, source=0, target=3): ... print(path) ... [0, 1, 2, 3] [0, 1, 3] [0, 2, 1, 3] [0, 2, 3] [0, 3] >>> paths = nx.all_simple_paths(G, source=0, target=3, cutoff=2) >>> print(list(paths)) [[0, 1, 3], [0, 2, 3], [0, 3]] Notes ----- This algorithm uses a modified depth-first search to generate the paths [1]_. A single path can be found in `O(V+E)` time but the number of simple paths in a graph can be very large, e.g. `O(n!)` in the complete graph of order n. References ---------- .. [1] R. Sedgewick, "Algorithms in C, Part 5: Graph Algorithms", Addison Wesley Professional, 3rd ed., 2001. See Also -------- all_shortest_paths, shortest_path """ if source not in G: raise nx.NetworkXError('source node %s not in graph'%source) if target not in G: raise nx.NetworkXError('target node %s not in graph'%target) if cutoff is None: cutoff = len(G)-1 if G.is_multigraph(): return _all_simple_paths_multigraph(G, source, target, cutoff=cutoff) else: return _all_simple_paths_graph(G, source, target, cutoff=cutoff)
def _all_simple_paths_graph(G, source, target, cutoff=None): if cutoff < 1: return visited = [source] stack = [iter(G[source])] while stack: children = stack[-1] child = next(children, None) if child is None: stack.pop() visited.pop() elif len(visited) < cutoff: if child == target: yield visited + [target] elif child not in visited: visited.append(child) stack.append(iter(G[child])) else: #len(visited) == cutoff: if child == target or target in children: yield visited + [target] stack.pop() visited.pop() def _all_simple_paths_multigraph(G, source, target, cutoff=None): if cutoff < 1: return visited = [source] stack = [(v for u,v in G.edges(source))] while stack: children = stack[-1] child = next(children, None) if child is None: stack.pop() visited.pop() elif len(visited) < cutoff: if child == target: yield visited + [target] elif child not in visited: visited.append(child) stack.append((v for u,v in G.edges(child))) else: #len(visited) == cutoff: count = ([child]+list(children)).count(target) for i in range(count): yield visited + [target] stack.pop() visited.pop()