# Source code for networkx.algorithms.shortest_paths.unweighted

# -*- coding: utf-8 -*-
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#
# Author:  Aric Hagberg <hagberg@lanl.gov>
"""
Shortest path algorithms for unweighted graphs.
"""
import networkx as nx

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

[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 : dict Dict keyed by node to shortest path length to source. Examples -------- >>> G = nx.path_graph(5) >>> length = nx.single_source_shortest_path_length(G, 0) >>> length[4] 4 >>> for node in length: ... print('{}: {}'.format(node, length[node])) 0: 0 1: 1 2: 2 3: 3 4: 4 See Also -------- shortest_path_length """ if source not in G: raise nx.NodeNotFound('Source {} is not in G'.format(source)) if cutoff is None: cutoff = float('inf') nextlevel = {source: 1} return dict(_single_shortest_path_length(G.adj, nextlevel, cutoff))
def _single_shortest_path_length(adj, firstlevel, cutoff): """Yields (node, level) in a breadth first search Shortest Path Length helper function Parameters ---------- adj : dict Adjacency dict or view firstlevel : dict starting nodes, e.g. {source: 1} or {target: 1} cutoff : int or float level at which we stop the process """ seen = {} # level (number of hops) when seen in BFS level = 0 # the current level nextlevel = firstlevel # dict of nodes to check at next level while nextlevel and cutoff >= level: 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(adj[v]) # add neighbors of v yield (v, level) level += 1 del seen
[docs]def single_target_shortest_path_length(G, target, cutoff=None): """Compute the shortest path lengths to target from all reachable nodes. Parameters ---------- G : NetworkX graph target : node Target node for path cutoff : integer, optional Depth to stop the search. Only paths of length <= cutoff are returned. Returns ------- lengths : iterator (source, shortest path length) iterator Examples -------- >>> G = nx.path_graph(5, create_using=nx.DiGraph()) >>> length = dict(nx.single_target_shortest_path_length(G, 4)) >>> length[0] 4 >>> for node in range(5): ... print('{}: {}'.format(node, length[node])) 0: 4 1: 3 2: 2 3: 1 4: 0 See Also -------- single_source_shortest_path_length, shortest_path_length """ if target not in G: raise nx.NodeNotFound('Target {} is not in G'.format(target)) if cutoff is None: cutoff = float('inf') # handle either directed or undirected adj = G.pred if G.is_directed() else G.adj nextlevel = {target: 1} return _single_shortest_path_length(adj, nextlevel, cutoff)
[docs]def all_pairs_shortest_path_length(G, cutoff=None): """Computes the shortest path lengths between all nodes in G. Parameters ---------- G : NetworkX graph cutoff : integer, optional Depth at which to stop the search. Only paths of length at most cutoff are returned. Returns ------- lengths : iterator (source, dictionary) iterator with dictionary keyed by target and shortest path length as the key value. Notes ----- The iterator returned only has reachable node pairs. Examples -------- >>> G = nx.path_graph(5) >>> length = dict(nx.all_pairs_shortest_path_length(G)) >>> for node in [0, 1, 2, 3, 4]: ... print('1 - {}: {}'.format(node, length[1][node])) 1 - 0: 1 1 - 1: 0 1 - 2: 1 1 - 3: 2 1 - 4: 3 >>> length[3][2] 1 >>> length[2][2] 0 """ length = single_source_shortest_path_length # TODO This can be trivially parallelized. for n in G: yield (n, length(G, n, cutoff=cutoff))
[docs]def bidirectional_shortest_path(G, source, target): """Returns 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). """ if source not in G or target not in G: msg = 'Either source {} or target {} is not in G' raise nx.NodeNotFound(msg.format(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 source to w while w is not None: path.append(w) w = pred[w] path.reverse() # from w to target w = succ[path[-1]] while w is not None: path.append(w) w = succ[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.pred Gsucc = G.succ else: Gpred = G.adj Gsucc = G.adj # 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: # path found return pred, succ, w 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: # found path return pred, succ, w 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 """ if source not in G: raise nx.NodeNotFound("Source {} not in G".format(source)) def join(p1, p2): return p1 + p2 if cutoff is None: cutoff = float('inf') nextlevel = {source: 1} # list of nodes to check at next level paths = {source: [source]} # paths dictionary (paths to key from source) return dict(_single_shortest_path(G.adj, nextlevel, paths, cutoff, join))
def _single_shortest_path(adj, firstlevel, paths, cutoff, join): """Returns shortest paths Shortest Path helper function Parameters ---------- adj : dict Adjacency dict or view firstlevel : dict starting nodes, e.g. {source: 1} or {target: 1} paths : dict paths for starting nodes, e.g. {source: [source]} cutoff : int or float level at which we stop the process join : function function to construct a path from two partial paths. Requires two list inputs p1 and p2, and returns a list. Usually returns p1 + p2 (forward from source) or p2 + p1 (backward from target) """ level = 0 # the current level nextlevel = firstlevel while nextlevel and cutoff > level: thislevel = nextlevel nextlevel = {} for v in thislevel: for w in adj[v]: if w not in paths: paths[w] = join(paths[v], [w]) nextlevel[w] = 1 level += 1 return paths
[docs]def single_target_shortest_path(G, target, cutoff=None): """Compute shortest path to target from all nodes that reach target. Parameters ---------- G : NetworkX graph target : node label Target 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, create_using=nx.DiGraph()) >>> path = nx.single_target_shortest_path(G, 4) >>> path[0] [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, single_source_shortest_path """ if target not in G: raise nx.NodeNotFound("Target {} not in G".format(target)) def join(p1, p2): return p2 + p1 # handle undirected graphs adj = G.pred if G.is_directed() else G.adj if cutoff is None: cutoff = float('inf') nextlevel = {target: 1} # list of nodes to check at next level paths = {target: [target]} # paths dictionary (paths to key from source) return dict(_single_shortest_path(adj, nextlevel, paths, cutoff, join))
[docs]def all_pairs_shortest_path(G, cutoff=None): """Compute shortest paths between all nodes. Parameters ---------- G : NetworkX graph cutoff : integer, optional Depth at which to stop the search. Only paths of length at most cutoff are returned. Returns ------- lengths : dictionary Dictionary, keyed by source and target, of shortest paths. Examples -------- >>> G = nx.path_graph(5) >>> path = dict(nx.all_pairs_shortest_path(G)) >>> print(path[0][4]) [0, 1, 2, 3, 4] See Also -------- floyd_warshall() """ # TODO This can be trivially parallelized. for n in G: yield (n, single_source_shortest_path(G, n, cutoff=cutoff))
[docs]def predecessor(G, source, target=None, cutoff=None, return_seen=None): """Returns dict 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) >>> list(G) [0, 1, 2, 3] >>> nx.predecessor(G, 0) {0: [], 1: [0], 2: [1], 3: [2]} """ if source not in G: raise nx.NodeNotFound("Source {} not in G".format(source)) 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 target not in pred: return ([], -1) # No predecessor return (pred[target], seen[target]) else: if target not in pred: return [] # No predecessor return pred[target] else: if return_seen: return (pred, seen) else: return pred