# breadth_first_search.py - breadth-first traversal of a graph # # Copyright (C) 2004-2017 NetworkX Developers # Aric Hagberg # Dan Schult # Pieter Swart # # This file is part of NetworkX. # # NetworkX is distributed under a BSD license; see LICENSE.txt for more # information. # # Authors: # Aric Hagberg # """Basic algorithms for breadth-first searching the nodes of a graph.""" import networkx as nx from collections import deque __all__ = ['bfs_edges', 'bfs_tree', 'bfs_predecessors', 'bfs_successors'] def generic_bfs_edges(G, source, neighbors=None): """Iterate over edges in a breadth-first search. The breadth-first search begins at `source` and enqueues the neighbors of newly visited nodes specified by the `neighbors` function. Parameters ---------- G : NetworkX graph source : node Starting node for the breadth-first search; this function iterates over only those edges in the component reachable from this node. neighbors : function A function that takes a newly visited node of the graph as input and returns an *iterator* (not just a list) of nodes that are neighbors of that node. If not specified, this is just the ``G.neighbors`` method, but in general it can be any function that returns an iterator over some or all of the neighbors of a given node, in any order. Yields ------ edge Edges in the breadth-first search starting from `source`. Examples -------- >>> G = nx.path_graph(3) >>> print(list(nx.bfs_edges(G,0))) [(0, 1), (1, 2)] Notes ----- This implementation is from `PADS`_, which was in the public domain when it was first accessed in July, 2004. .. _PADS: http://www.ics.uci.edu/~eppstein/PADS/BFS.py """ visited = {source} queue = deque([(source, neighbors(source))]) while queue: parent, children = queue[0] try: child = next(children) if child not in visited: yield parent, child visited.add(child) queue.append((child, neighbors(child))) except StopIteration: queue.popleft() def bfs_edges(G, source, reverse=False): """Iterate over edges in a breadth-first-search starting at source. Parameters ---------- G : NetworkX graph source : node Specify starting node for breadth-first search and return edges in the component reachable from source. reverse : bool, optional If True traverse a directed graph in the reverse direction Returns ------- edges: generator A generator of edges in the breadth-first-search. Examples -------- To get the edges in a breadth-first search:: >>> G = nx.path_graph(3) >>> list(nx.bfs_edges(G, 0)) [(0, 1), (1, 2)] To get the nodes in a breadth-first search order:: >>> G = nx.path_graph(3) >>> root = 2 >>> edges = nx.bfs_edges(G, root) >>> nodes = [root] + [v for u, v in edges] >>> nodes [2, 1, 0] Notes ----- Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py by D. Eppstein, July 2004. """ if reverse and G.is_directed(): successors = G.predecessors else: successors = G.neighbors # TODO In Python 3.3+, this should be `yield from ...` for e in generic_bfs_edges(G, source, successors): yield e def bfs_tree(G, source, reverse=False): """Return an oriented tree constructed from of a breadth-first-search starting at source. Parameters ---------- G : NetworkX graph source : node Specify starting node for breadth-first search and return edges in the component reachable from source. reverse : bool, optional If True traverse a directed graph in the reverse direction Returns ------- T: NetworkX DiGraph An oriented tree Examples -------- >>> G = nx.path_graph(3) >>> print(list(nx.bfs_tree(G,1).edges())) [(1, 0), (1, 2)] Notes ----- Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py by D. Eppstein, July 2004. """ T = nx.DiGraph() T.add_node(source) T.add_edges_from(bfs_edges(G, source, reverse=reverse)) return T def bfs_predecessors(G, source): """Returns an iterator of predecessors in breadth-first-search from source. Parameters ---------- G : NetworkX graph source : node Specify starting node for breadth-first search and return edges in the component reachable from source. Returns ------- pred: iterator (node, predecessors) iterator where predecessors is the list of predecessors of the node. Examples -------- >>> G = nx.path_graph(3) >>> print(dict(nx.bfs_predecessors(G, 0))) {1: 0, 2: 1} >>> H = nx.Graph() >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) >>> dict(nx.bfs_predecessors(H, 0)) {1: 0, 2: 0, 3: 1, 4: 1, 5: 2, 6: 2} Notes ----- Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py by D. Eppstein, July 2004. """ for s, t in bfs_edges(G, source): yield (t, s) def bfs_successors(G, source): """Returns an iterator of successors in breadth-first-search from source. Parameters ---------- G : NetworkX graph source : node Specify starting node for breadth-first search and return edges in the component reachable from source. Returns ------- succ: iterator (node, successors) iterator where successors is the list of successors of the node. Examples -------- >>> G = nx.path_graph(3) >>> print(dict(nx.bfs_successors(G,0))) {0: [1], 1: [2]} >>> H = nx.Graph() >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) >>> dict(nx.bfs_successors(H, 0)) {0: [1, 2], 1: [3, 4], 2: [5, 6]} Notes ----- Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py by D. Eppstein, July 2004. """ parent = source children = [] for p, c in bfs_edges(G, source): if p == parent: children.append(c) continue yield (parent, children) children = [c] parent = p yield (parent, children)