Source code for networkx.algorithms.approximation.steinertree

from itertools import chain

from networkx.utils import pairwise, not_implemented_for
import networkx as nx

__all__ = ['metric_closure', 'steiner_tree']


[docs]@not_implemented_for('directed') def metric_closure(G, weight='weight'): """ Return the metric closure of a graph. The metric closure of a graph *G* is the complete graph in which each edge is weighted by the shortest path distance between the nodes in *G* . Parameters ---------- G : NetworkX graph Returns ------- NetworkX graph Metric closure of the graph `G`. """ M = nx.Graph() Gnodes = set(G) # check for connected graph while processing first node all_paths_iter = nx.all_pairs_dijkstra(G, weight=weight) u, (distance, path) = next(all_paths_iter) if Gnodes - set(distance): msg = "G is not a connected graph. metric_closure is not defined." raise nx.NetworkXError(msg) Gnodes.remove(u) for v in Gnodes: M.add_edge(u, v, distance=distance[v], path=path[v]) # first node done -- now process the rest for u, (distance, path) in all_paths_iter: Gnodes.remove(u) for v in Gnodes: M.add_edge(u, v, distance=distance[v], path=path[v]) return M
[docs]@not_implemented_for('multigraph') @not_implemented_for('directed') def steiner_tree(G, terminal_nodes, weight='weight'): """ Return an approximation to the minimum Steiner tree of a graph. Parameters ---------- G : NetworkX graph terminal_nodes : list A list of terminal nodes for which minimum steiner tree is to be found. Returns ------- NetworkX graph Approximation to the minimum steiner tree of `G` induced by `terminal_nodes` . Notes ----- Steiner tree can be approximated by computing the minimum spanning tree of the subgraph of the metric closure of the graph induced by the terminal nodes, where the metric closure of *G* is the complete graph in which each edge is weighted by the shortest path distance between the nodes in *G* . This algorithm produces a tree whose weight is within a (2 - (2 / t)) factor of the weight of the optimal Steiner tree where *t* is number of terminal nodes. """ # M is the subgraph of the metric closure induced by the terminal nodes of # G. M = metric_closure(G, weight=weight) # Use the 'distance' attribute of each edge provided by the metric closure # graph. H = M.subgraph(terminal_nodes) mst_edges = nx.minimum_spanning_edges(H, weight='distance', data=True) # Create an iterator over each edge in each shortest path; repeats are okay edges = chain.from_iterable(pairwise(d['path']) for u, v, d in mst_edges) T = G.edge_subgraph(edges) return T