Source code for networkx.algorithms.traversal.breadth_first_search

"""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",
    "descendants_at_distance",
]


def generic_bfs_edges(G, source, neighbors=None, depth_limit=None, sort_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.

    depth_limit : int, optional(default=len(G))
        Specify the maximum search depth

    sort_neighbors : function
        A function that takes the list of neighbors of given node as input, and
        returns an *iterator* over these neighbors but with custom ordering.

    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)]
    >>> print(list(nx.bfs_edges(G, source=0, depth_limit=1)))
    [(0, 1)]

    Notes
    -----
    This implementation is from `PADS`_, which was in the public domain
    when it was first accessed in July, 2004.  The modifications
    to allow depth limits are based on the Wikipedia article
    "`Depth-limited-search`_".

    .. _PADS: http://www.ics.uci.edu/~eppstein/PADS/BFS.py
    .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search
    """
    if callable(sort_neighbors):
        _neighbors = neighbors
        neighbors = lambda node: iter(sort_neighbors(_neighbors(node)))

    visited = {source}
    if depth_limit is None:
        depth_limit = len(G)
    queue = deque([(source, depth_limit, neighbors(source))])
    while queue:
        parent, depth_now, children = queue[0]
        try:
            child = next(children)
            if child not in visited:
                yield parent, child
                visited.add(child)
                if depth_now > 1:
                    queue.append((child, depth_now - 1, neighbors(child)))
        except StopIteration:
            queue.popleft()


[docs]def bfs_edges(G, source, reverse=False, depth_limit=None, sort_neighbors=None): """Iterate over edges in a breadth-first-search starting at source. Parameters ---------- G : NetworkX graph source : node Specify starting node for breadth-first search; this function iterates over only those edges in the component reachable from this node. reverse : bool, optional If True traverse a directed graph in the reverse direction depth_limit : int, optional(default=len(G)) Specify the maximum search depth sort_neighbors : function A function that takes the list of neighbors of given node as input, and returns an *iterator* over these neighbors but with custom ordering. Yields ------ edge: 2-tuple of nodes Yields edges resulting from 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)] >>> list(nx.bfs_edges(G, source=0, depth_limit=1)) [(0, 1)] 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 ----- The naming of this function is very similar to :func:`~networkx.algorithms.traversal.edgebfs.edge_bfs`. The difference is that ``edge_bfs`` yields edges even if they extend back to an already explored node while this generator yields the edges of the tree that results from a breadth-first-search (BFS) so no edges are reported if they extend to already explored nodes. That means ``edge_bfs`` reports all edges while ``bfs_edges`` only reports those traversed by a node-based BFS. Yet another description is that ``bfs_edges`` reports the edges traversed during BFS while ``edge_bfs`` reports all edges in the order they are explored. Based on the breadth-first search implementation in PADS [1]_ by D. Eppstein, July 2004; with modifications to allow depth limits as described in [2]_. References ---------- .. [1] http://www.ics.uci.edu/~eppstein/PADS/BFS.py. .. [2] https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- bfs_tree :func:`~networkx.algorithms.traversal.depth_first_search.dfs_edges` :func:`~networkx.algorithms.traversal.edgebfs.edge_bfs` """ if reverse and G.is_directed(): successors = G.predecessors else: successors = G.neighbors yield from generic_bfs_edges(G, source, successors, depth_limit, sort_neighbors)
[docs]def bfs_tree(G, source, reverse=False, depth_limit=None, sort_neighbors=None): """Returns 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 reverse : bool, optional If True traverse a directed graph in the reverse direction depth_limit : int, optional(default=len(G)) Specify the maximum search depth sort_neighbors : function A function that takes the list of neighbors of given node as input, and returns an *iterator* over these neighbors but with custom ordering. 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)] >>> H = nx.Graph() >>> nx.add_path(H, [0, 1, 2, 3, 4, 5, 6]) >>> nx.add_path(H, [2, 7, 8, 9, 10]) >>> print(sorted(list(nx.bfs_tree(H, source=3, depth_limit=3).edges()))) [(1, 0), (2, 1), (2, 7), (3, 2), (3, 4), (4, 5), (5, 6), (7, 8)] Notes ----- Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py by D. Eppstein, July 2004. The modifications to allow depth limits based on the Wikipedia article "`Depth-limited-search`_". .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- dfs_tree bfs_edges edge_bfs """ T = nx.DiGraph() T.add_node(source) edges_gen = bfs_edges( G, source, reverse=reverse, depth_limit=depth_limit, sort_neighbors=sort_neighbors, ) T.add_edges_from(edges_gen) return T
[docs]def bfs_predecessors(G, source, depth_limit=None, sort_neighbors=None): """Returns an iterator of predecessors in breadth-first-search from source. Parameters ---------- G : NetworkX graph source : node Specify starting node for breadth-first search depth_limit : int, optional(default=len(G)) Specify the maximum search depth sort_neighbors : function A function that takes the list of neighbors of given node as input, and returns an *iterator* over these neighbors but with custom ordering. Returns ------- pred: iterator (node, predecessor) iterator where `predecessor` is the predecessor of `node` in a breadth first search starting from `source`. 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)]) >>> print(dict(nx.bfs_predecessors(H, 0))) {1: 0, 2: 0, 3: 1, 4: 1, 5: 2, 6: 2} >>> M = nx.Graph() >>> nx.add_path(M, [0, 1, 2, 3, 4, 5, 6]) >>> nx.add_path(M, [2, 7, 8, 9, 10]) >>> print(sorted(nx.bfs_predecessors(M, source=1, depth_limit=3))) [(0, 1), (2, 1), (3, 2), (4, 3), (7, 2), (8, 7)] >>> N = nx.DiGraph() >>> nx.add_path(N, [0, 1, 2, 3, 4, 7]) >>> nx.add_path(N, [3, 5, 6, 7]) >>> print(sorted(nx.bfs_predecessors(N, source=2))) [(3, 2), (4, 3), (5, 3), (6, 5), (7, 4)] Notes ----- Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py by D. Eppstein, July 2004. The modifications to allow depth limits based on the Wikipedia article "`Depth-limited-search`_". .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- bfs_tree bfs_edges edge_bfs """ for s, t in bfs_edges( G, source, depth_limit=depth_limit, sort_neighbors=sort_neighbors ): yield (t, s)
[docs]def bfs_successors(G, source, depth_limit=None, sort_neighbors=None): """Returns an iterator of successors in breadth-first-search from source. Parameters ---------- G : NetworkX graph source : node Specify starting node for breadth-first search depth_limit : int, optional(default=len(G)) Specify the maximum search depth sort_neighbors : function A function that takes the list of neighbors of given node as input, and returns an *iterator* over these neighbors but with custom ordering. Returns ------- succ: iterator (node, successors) iterator where `successors` is the non-empty list of successors of `node` in a breadth first search from `source`. To appear in the iterator, `node` must have successors. 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)]) >>> print(dict(nx.bfs_successors(H, 0))) {0: [1, 2], 1: [3, 4], 2: [5, 6]} >>> G = nx.Graph() >>> nx.add_path(G, [0, 1, 2, 3, 4, 5, 6]) >>> nx.add_path(G, [2, 7, 8, 9, 10]) >>> print(dict(nx.bfs_successors(G, source=1, depth_limit=3))) {1: [0, 2], 2: [3, 7], 3: [4], 7: [8]} >>> G = nx.DiGraph() >>> nx.add_path(G, [0, 1, 2, 3, 4, 5]) >>> print(dict(nx.bfs_successors(G, source=3))) {3: [4], 4: [5]} Notes ----- Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py by D. Eppstein, July 2004.The modifications to allow depth limits based on the Wikipedia article "`Depth-limited-search`_". .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- bfs_tree bfs_edges edge_bfs """ parent = source children = [] for p, c in bfs_edges( G, source, depth_limit=depth_limit, sort_neighbors=sort_neighbors ): if p == parent: children.append(c) continue yield (parent, children) children = [c] parent = p yield (parent, children)
[docs]def descendants_at_distance(G, source, distance): """Returns all nodes at a fixed `distance` from `source` in `G`. Parameters ---------- G : NetworkX graph A graph source : node in `G` distance : the distance of the wanted nodes from `source` Returns ------- set() The descendants of `source` in `G` at the given `distance` from `source` """ if not G.has_node(source): raise nx.NetworkXError(f"The node {source} is not in the graph.") current_distance = 0 queue = {source} visited = {source} # this is basically BFS, except that the queue only stores the nodes at # current_distance from source at each iteration while queue: if current_distance == distance: return queue current_distance += 1 next_vertices = set() for vertex in queue: for child in G[vertex]: if child not in visited: visited.add(child) next_vertices.add(child) queue = next_vertices return set()