# -*- coding: utf-8 -*- """ Compute the shortest paths and path lengths between nodes in the graph. """ __author__ = """Aric Hagberg (hagberg@lanl.gov)""" # Copyright (C) 2004-2010 by # Aric Hagberg # Dan Schult # Pieter Swart # All rights reserved. # BSD license. __all__ = ['shortest_path', 'shortest_path_length', 'average_shortest_path_length'] import networkx as nx def shortest_path(G,source=None,target=None,weighted=False): """Compute shortest paths in the graph. Parameters ---------- G : NetworkX graph source : node, optional Starting node for path. If not specified compute shortest paths for all connected node pairs. target : node, optional Ending node for path. If not specified compute shortest paths for every node reachable from the source. weighted : bool, optional If True consider weighted edges when finding shortest path. Returns ------- path: list or dictionary If the source and target are both specified return a single list of nodes in a shortest path. If only the source is specified return a dictionary keyed by targets with a list of nodes in a shortest path. If neither the source or target is specified return a dictionary of dictionaries with path[source][target]=[list of nodes in path]. Examples -------- >>> G=nx.path_graph(5) >>> print nx.shortest_path(G,source=0,target=4) [0, 1, 2, 3, 4] >>> p=nx.shortest_path(G,source=0) # target not specified >>> p[4] [0, 1, 2, 3, 4] >>> p=nx.shortest_path(G) # source,target not specified >>> p[0][4] [0, 1, 2, 3, 4] Notes ----- There may be more than one shortest path between a source and target. This returns only one of them. If weighted=True and the graph has no 'weight' edge attribute the value 1 will be used. """ if source is None: if target is None: if weighted: paths=nx.all_pairs_dijkstra_path(G) else: paths=nx.all_pairs_shortest_path(G) else: raise nx.NetworkXError(\ "Target given but no source specified.") else: # source specified if target is None: if weighted: paths=nx.single_source_dijkstra_path(G,source) else: paths=nx.single_source_shortest_path(G,source) else: # shortest source-target path if weighted: paths=nx.dijkstra_path(G,source,target) else: paths=nx.bidirectional_shortest_path(G,source,target) return paths def shortest_path_length(G,source=None,target=None,weighted=False): """Compute shortest path lengths in the graph. This function can compute the single source shortest path lengths by specifying only the source or all pairs shortest path lengths by specifying neither the source or target. Parameters ---------- G : NetworkX graph source : node, optional Starting node for path. If not specified compute shortest pats lenghts for all connected node pairs. target : node, optional Ending node for path. If not specified compute shortest path lenghts for every node reachable from the source. weighted : bool, optional If True consider weighted edges when finding shortest path length. Returns ------- length : number, or container of numbers If the source and target are both specified return a single number for the shortest path. If only the source is specified return a dictionary keyed by targets with a the shortest path as keys. If neither the source or target is specified return a dictionary of dictionaries with length[source][target]=value. Raises ------ NetworkXError If no path exists between source and target. Examples -------- >>> G=nx.path_graph(5) >>> print nx.shortest_path_length(G,source=0,target=4) 4 >>> p=nx.shortest_path_length(G,source=0) # target not specified >>> p[4] 4 >>> p=nx.shortest_path_length(G) # source,target not specified >>> p[0][4] 4 Notes ----- If weighted=True and the graph has no 'weight' edge attribute the value 1 will be used. """ if source is None: if target is None: if weighted: paths=nx.all_pairs_dijkstra_path_length(G) else: paths=nx.all_pairs_shortest_path_length(G) else: raise nx.NetworkXError(\ "Target given but no source specified.") else: # source specified if target is None: if weighted: paths=nx.single_source_dijkstra_path_length(G,source) else: paths=nx.single_source_shortest_path_length(G,source) else: # shortest source-target path if weighted: paths=nx.dijkstra_path_length(G,source,target) else: p=nx.bidirectional_shortest_path(G,source,target) if p is False: raise nx.NetworkXError(\ "No path from %s to %s."%(source,target)) paths=len(p)-1 return paths def average_shortest_path_length(G,weighted=False): """ Return the average shortest path length. The average shortest path length is the sum of path lengths d(u,v) between all pairs of nodes (assuming the length is zero if v is not reachable from v) normalized by n*(n-1) where n is the number of nodes in G. Parameters ---------- G : NetworkX graph weighted : bool, optional, default=False If True use edge weights on path. Examples -------- >>> G=nx.path_graph(5) >>> print nx.average_shortest_path_length(G) 2.0 Notes ----- If weighted=True and the graph has no 'weight' edge attribute the value 1 will be used. """ if weighted: path_length=nx.single_source_dijkstra_path_length else: path_length=nx.single_source_shortest_path_length avg=0.0 for n in G: l=path_length(G,n).values() avg+=float(sum(l))/len(l) return avg/(len(G)-1)