Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

Source code for networkx.algorithms.traversal.depth_first_search

"""Basic algorithms for depth-first searching the nodes of a graph."""
import networkx as nx
from collections import defaultdict

__all__ = [
    "dfs_edges",
    "dfs_tree",
    "dfs_predecessors",
    "dfs_successors",
    "dfs_preorder_nodes",
    "dfs_postorder_nodes",
    "dfs_labeled_edges",
]


[docs]def dfs_edges(G, source=None, depth_limit=None): """Iterate over edges in a depth-first-search (DFS). Perform a depth-first-search over the nodes of G and yield the edges in order. This may not generate all edges in G (see edge_dfs). Parameters ---------- G : NetworkX graph source : node, optional Specify starting node for depth-first search and return edges in the component reachable from source. depth_limit : int, optional (default=len(G)) Specify the maximum search depth. Returns ------- edges: generator A generator of edges in the depth-first-search. Examples -------- >>> G = nx.path_graph(5) >>> list(nx.dfs_edges(G, source=0)) [(0, 1), (1, 2), (2, 3), (3, 4)] >>> list(nx.dfs_edges(G, source=0, depth_limit=2)) [(0, 1), (1, 2)] Notes ----- If a source is not specified then a source is chosen arbitrarily and repeatedly until all components in the graph are searched. The implementation of this function is adapted from David Eppstein's depth-first search function in `PADS`_, with modifications to allow depth limits based on the Wikipedia article "`Depth-limited search`_". .. _PADS: http://www.ics.uci.edu/~eppstein/PADS .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- dfs_preorder_nodes dfs_postorder_nodes dfs_labeled_edges edge_dfs bfs_edges """ if source is None: # edges for all components nodes = G else: # edges for components with source nodes = [source] visited = set() if depth_limit is None: depth_limit = len(G) for start in nodes: if start in visited: continue visited.add(start) stack = [(start, depth_limit, iter(G[start]))] while stack: parent, depth_now, children = stack[-1] try: child = next(children) if child not in visited: yield parent, child visited.add(child) if depth_now > 1: stack.append((child, depth_now - 1, iter(G[child]))) except StopIteration: stack.pop()
[docs]def dfs_tree(G, source=None, depth_limit=None): """Returns oriented tree constructed from a depth-first-search from source. Parameters ---------- G : NetworkX graph source : node, optional Specify starting node for depth-first search. depth_limit : int, optional (default=len(G)) Specify the maximum search depth. Returns ------- T : NetworkX DiGraph An oriented tree Examples -------- >>> G = nx.path_graph(5) >>> T = nx.dfs_tree(G, source=0, depth_limit=2) >>> list(T.edges()) [(0, 1), (1, 2)] >>> T = nx.dfs_tree(G, source=0) >>> list(T.edges()) [(0, 1), (1, 2), (2, 3), (3, 4)] See Also -------- dfs_preorder_nodes dfs_postorder_nodes dfs_labeled_edges edge_dfs bfs_tree """ T = nx.DiGraph() if source is None: T.add_nodes_from(G) else: T.add_node(source) T.add_edges_from(dfs_edges(G, source, depth_limit)) return T
[docs]def dfs_predecessors(G, source=None, depth_limit=None): """Returns dictionary of predecessors in depth-first-search from source. Parameters ---------- G : NetworkX graph source : node, optional Specify starting node for depth-first search. depth_limit : int, optional (default=len(G)) Specify the maximum search depth. Returns ------- pred: dict A dictionary with nodes as keys and predecessor nodes as values. Examples -------- >>> G = nx.path_graph(4) >>> nx.dfs_predecessors(G, source=0) {1: 0, 2: 1, 3: 2} >>> nx.dfs_predecessors(G, source=0, depth_limit=2) {1: 0, 2: 1} Notes ----- If a source is not specified then a source is chosen arbitrarily and repeatedly until all components in the graph are searched. The implementation of this function is adapted from David Eppstein's depth-first search function in `PADS`_, with modifications to allow depth limits based on the Wikipedia article "`Depth-limited search`_". .. _PADS: http://www.ics.uci.edu/~eppstein/PADS .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- dfs_preorder_nodes dfs_postorder_nodes dfs_labeled_edges edge_dfs bfs_tree """ return {t: s for s, t in dfs_edges(G, source, depth_limit)}
[docs]def dfs_successors(G, source=None, depth_limit=None): """Returns dictionary of successors in depth-first-search from source. Parameters ---------- G : NetworkX graph source : node, optional Specify starting node for depth-first search. depth_limit : int, optional (default=len(G)) Specify the maximum search depth. Returns ------- succ: dict A dictionary with nodes as keys and list of successor nodes as values. Examples -------- >>> G = nx.path_graph(5) >>> nx.dfs_successors(G, source=0) {0: [1], 1: [2], 2: [3], 3: [4]} >>> nx.dfs_successors(G, source=0, depth_limit=2) {0: [1], 1: [2]} Notes ----- If a source is not specified then a source is chosen arbitrarily and repeatedly until all components in the graph are searched. The implementation of this function is adapted from David Eppstein's depth-first search function in `PADS`_, with modifications to allow depth limits based on the Wikipedia article "`Depth-limited search`_". .. _PADS: http://www.ics.uci.edu/~eppstein/PADS .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- dfs_preorder_nodes dfs_postorder_nodes dfs_labeled_edges edge_dfs bfs_tree """ d = defaultdict(list) for s, t in dfs_edges(G, source=source, depth_limit=depth_limit): d[s].append(t) return dict(d)
[docs]def dfs_postorder_nodes(G, source=None, depth_limit=None): """Generate nodes in a depth-first-search post-ordering starting at source. Parameters ---------- G : NetworkX graph source : node, optional Specify starting node for depth-first search. depth_limit : int, optional (default=len(G)) Specify the maximum search depth. Returns ------- nodes: generator A generator of nodes in a depth-first-search post-ordering. Examples -------- >>> G = nx.path_graph(5) >>> list(nx.dfs_postorder_nodes(G, source=0)) [4, 3, 2, 1, 0] >>> list(nx.dfs_postorder_nodes(G, source=0, depth_limit=2)) [1, 0] Notes ----- If a source is not specified then a source is chosen arbitrarily and repeatedly until all components in the graph are searched. The implementation of this function is adapted from David Eppstein's depth-first search function in `PADS`_, with modifications to allow depth limits based on the Wikipedia article "`Depth-limited search`_". .. _PADS: http://www.ics.uci.edu/~eppstein/PADS .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- dfs_edges dfs_preorder_nodes dfs_labeled_edges edge_dfs bfs_tree """ edges = nx.dfs_labeled_edges(G, source=source, depth_limit=depth_limit) return (v for u, v, d in edges if d == "reverse")
[docs]def dfs_preorder_nodes(G, source=None, depth_limit=None): """Generate nodes in a depth-first-search pre-ordering starting at source. Parameters ---------- G : NetworkX graph source : node, optional Specify starting node for depth-first search and return nodes in the component reachable from source. depth_limit : int, optional (default=len(G)) Specify the maximum search depth. Returns ------- nodes: generator A generator of nodes in a depth-first-search pre-ordering. Examples -------- >>> G = nx.path_graph(5) >>> list(nx.dfs_preorder_nodes(G, source=0)) [0, 1, 2, 3, 4] >>> list(nx.dfs_preorder_nodes(G, source=0, depth_limit=2)) [0, 1, 2] Notes ----- If a source is not specified then a source is chosen arbitrarily and repeatedly until all components in the graph are searched. The implementation of this function is adapted from David Eppstein's depth-first search function in `PADS`_, with modifications to allow depth limits based on the Wikipedia article "`Depth-limited search`_". .. _PADS: http://www.ics.uci.edu/~eppstein/PADS .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- dfs_edges dfs_postorder_nodes dfs_labeled_edges bfs_edges """ edges = nx.dfs_labeled_edges(G, source=source, depth_limit=depth_limit) return (v for u, v, d in edges if d == "forward")
[docs]def dfs_labeled_edges(G, source=None, depth_limit=None): """Iterate over edges in a depth-first-search (DFS) labeled by type. Parameters ---------- G : NetworkX graph source : node, optional Specify starting node for depth-first search and return edges in the component reachable from source. depth_limit : int, optional (default=len(G)) Specify the maximum search depth. Returns ------- edges: generator A generator of triples of the form (*u*, *v*, *d*), where (*u*, *v*) is the edge being explored in the depth-first search and *d* is one of the strings 'forward', 'nontree', or 'reverse'. A 'forward' edge is one in which *u* has been visited but *v* has not. A 'nontree' edge is one in which both *u* and *v* have been visited but the edge is not in the DFS tree. A 'reverse' edge is on in which both *u* and *v* have been visited and the edge is in the DFS tree. Examples -------- The labels reveal the complete transcript of the depth-first search algorithm in more detail than, for example, :func:`dfs_edges`:: >>> from pprint import pprint >>> >>> G = nx.DiGraph([(0, 1), (1, 2), (2, 1)]) >>> pprint(list(nx.dfs_labeled_edges(G, source=0))) [(0, 0, 'forward'), (0, 1, 'forward'), (1, 2, 'forward'), (2, 1, 'nontree'), (1, 2, 'reverse'), (0, 1, 'reverse'), (0, 0, 'reverse')] Notes ----- If a source is not specified then a source is chosen arbitrarily and repeatedly until all components in the graph are searched. The implementation of this function is adapted from David Eppstein's depth-first search function in `PADS`_, with modifications to allow depth limits based on the Wikipedia article "`Depth-limited search`_". .. _PADS: http://www.ics.uci.edu/~eppstein/PADS .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- dfs_edges dfs_preorder_nodes dfs_postorder_nodes """ # Based on http://www.ics.uci.edu/~eppstein/PADS/DFS.py # by D. Eppstein, July 2004. if source is None: # edges for all components nodes = G else: # edges for components with source nodes = [source] visited = set() if depth_limit is None: depth_limit = len(G) for start in nodes: if start in visited: continue yield start, start, "forward" visited.add(start) stack = [(start, depth_limit, iter(G[start]))] while stack: parent, depth_now, children = stack[-1] try: child = next(children) if child in visited: yield parent, child, "nontree" else: yield parent, child, "forward" visited.add(child) if depth_now > 1: stack.append((child, depth_now - 1, iter(G[child]))) except StopIteration: stack.pop() if stack: yield stack[-1][0], parent, "reverse" yield start, start, "reverse"