NetworkX

Source code for networkx.algorithms.shortest_paths.unweighted

# -*- coding: utf-8 -*-
"""
Shortest path algorithms for unweighted graphs.
"""
__author__ = """Aric Hagberg (hagberg@lanl.gov)"""
#    Copyright (C) 2004-2010 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.

__all__ = ['bidirectional_shortest_path',
           'single_source_shortest_path',
           'single_source_shortest_path_length',
           'all_pairs_shortest_path',
           'all_pairs_shortest_path_length',
           'predecessor']


import networkx as nx

[docs]def single_source_shortest_path_length(G,source,cutoff=None): """Compute the shortest path lengths from source to all reachable nodes. Parameters ---------- G : NetworkX graph source : node Starting node for path cutoff : integer, optional Depth to stop the search. Only paths of length <= cutoff are returned. Returns ------- lengths : dictionary Dictionary of shortest path lengths keyed by target. Examples -------- >>> G=nx.path_graph(5) >>> length=nx.single_source_shortest_path_length(G,0) >>> length[4] 4 >>> print(length) {0: 0, 1: 1, 2: 2, 3: 3, 4: 4} See Also -------- shortest_path_length """ seen={} # level (number of hops) when seen in BFS level=0 # the current level nextlevel={source:1} # dict of nodes to check at next level while nextlevel: thislevel=nextlevel # advance to next level nextlevel={} # and start a new list (fringe) for v in thislevel: if v not in seen: seen[v]=level # set the level of vertex v nextlevel.update(G[v]) # add neighbors of v if (cutoff is not None and cutoff <= level): break level=level+1 return seen # return all path lengths as dictionary
[docs]def all_pairs_shortest_path_length(G,cutoff=None): """ Compute the shortest path lengths between all nodes in G. Parameters ---------- G : NetworkX graph cutoff : integer, optional depth to stop the search. Only paths of length <= cutoff are returned. Returns ------- lengths : dictionary Dictionary of shortest path lengths keyed by source and target. Notes ----- The dictionary returned only has keys for reachable node pairs. Examples -------- >>> G=nx.path_graph(5) >>> length=nx.all_pairs_shortest_path_length(G) >>> print(length[1][4]) 3 >>> length[1] {0: 1, 1: 0, 2: 1, 3: 2, 4: 3} """ paths={} for n in G: paths[n]=single_source_shortest_path_length(G,n,cutoff=cutoff) return paths
def bidirectional_shortest_path(G,source,target): """Return a list of nodes in a shortest path between source and target. Parameters ---------- G : NetworkX graph source : node label starting node for path target : node label ending node for path Returns ------- path: list List of nodes in a path from source to target. Raises ------ NetworkXNoPath If no path exists between source and target. See Also -------- shortest_path Notes ----- This algorithm is used by shortest_path(G,source,target). """ # call helper to do the real work results=_bidirectional_pred_succ(G,source,target) pred,succ,w=results # build path from pred+w+succ path=[] # from w to target while w is not None: path.append(w) w=succ[w] # from source to w w=pred[path[0]] while w is not None: path.insert(0,w) w=pred[w] return path def _bidirectional_pred_succ(G, source, target): """Bidirectional shortest path helper. Returns (pred,succ,w) where pred is a dictionary of predecessors from w to the source, and succ is a dictionary of successors from w to the target. """ # does BFS from both source and target and meets in the middle if target == source: return ({target:None},{source:None},source) # handle either directed or undirected if G.is_directed(): Gpred=G.predecessors_iter Gsucc=G.successors_iter else: Gpred=G.neighbors_iter Gsucc=G.neighbors_iter # predecesssor and successors in search pred={source:None} succ={target:None} # initialize fringes, start with forward forward_fringe=[source] reverse_fringe=[target] while forward_fringe and reverse_fringe: if len(forward_fringe) <= len(reverse_fringe): this_level=forward_fringe forward_fringe=[] for v in this_level: for w in Gsucc(v): if w not in pred: forward_fringe.append(w) pred[w]=v if w in succ: return pred,succ,w # found path else: this_level=reverse_fringe reverse_fringe=[] for v in this_level: for w in Gpred(v): if w not in succ: succ[w]=v reverse_fringe.append(w) if w in pred: return pred,succ,w # found path raise nx.NetworkXNoPath("No path between %s and %s." % (source, target))
[docs]def single_source_shortest_path(G,source,cutoff=None): """Compute shortest path between source and all other nodes reachable from source. Parameters ---------- G : NetworkX graph source : node label Starting node for path cutoff : integer, optional Depth to stop the search. Only paths of length <= cutoff are returned. Returns ------- lengths : dictionary Dictionary, keyed by target, of shortest paths. Examples -------- >>> G=nx.path_graph(5) >>> path=nx.single_source_shortest_path(G,0) >>> path[4] [0, 1, 2, 3, 4] Notes ----- The shortest path is not necessarily unique. So there can be multiple paths between the source and each target node, all of which have the same 'shortest' length. For each target node, this function returns only one of those paths. See Also -------- shortest_path """ level=0 # the current level nextlevel={source:1} # list of nodes to check at next level paths={source:[source]} # paths dictionary (paths to key from source) if cutoff==0: return paths while nextlevel: thislevel=nextlevel nextlevel={} for v in thislevel: for w in G[v]: if w not in paths: paths[w]=paths[v]+[w] nextlevel[w]=1 level=level+1 if (cutoff is not None and cutoff <= level): break return paths
[docs]def all_pairs_shortest_path(G,cutoff=None): """ Compute shortest paths between all nodes. Parameters ---------- G : NetworkX graph cutoff : integer, optional Depth to stop the search. Only paths of length <= cutoff are returned. Returns ------- lengths : dictionary Dictionary, keyed by source and target, of shortest paths. Examples -------- >>> G=nx.path_graph(5) >>> path=nx.all_pairs_shortest_path(G) >>> print(path[0][4]) [0, 1, 2, 3, 4] See Also -------- floyd_warshall() """ paths={} for n in G: paths[n]=single_source_shortest_path(G,n,cutoff=cutoff) return paths
[docs]def predecessor(G,source,target=None,cutoff=None,return_seen=None): """ Returns dictionary of predecessors for the path from source to all nodes in G. Parameters ---------- G : NetworkX graph source : node label Starting node for path target : node label, optional Ending node for path. If provided only predecessors between source and target are returned cutoff : integer, optional Depth to stop the search. Only paths of length <= cutoff are returned. Returns ------- pred : dictionary Dictionary, keyed by node, of predecessors in the shortest path. Examples -------- >>> G=nx.path_graph(4) >>> print(G.nodes()) [0, 1, 2, 3] >>> nx.predecessor(G,0) {0: [], 1: [0], 2: [1], 3: [2]} """ level=0 # the current level nextlevel=[source] # list of nodes to check at next level seen={source:level} # level (number of hops) when seen in BFS pred={source:[]} # predecessor dictionary while nextlevel: level=level+1 thislevel=nextlevel nextlevel=[] for v in thislevel: for w in G[v]: if w not in seen: pred[w]=[v] seen[w]=level nextlevel.append(w) elif (seen[w]==level):# add v to predecessor list if it pred[w].append(v) # is at the correct level if (cutoff and cutoff <= level): break if target is not None: if return_seen: if not target in pred: return ([],-1) # No predecessor return (pred[target],seen[target]) else: if not target in pred: return [] # No predecessor return pred[target] else: if return_seen: return (pred,seen) else: return pred