Source code for networkx.algorithms.centrality.current_flow_closeness

"""Current-flow closeness centrality measures."""
import networkx as nx
from networkx.algorithms.centrality.flow_matrix import (
from networkx.utils import not_implemented_for, reverse_cuthill_mckee_ordering

__all__ = ["current_flow_closeness_centrality", "information_centrality"]

[docs] @not_implemented_for("directed") @nx._dispatchable(edge_attrs="weight") def current_flow_closeness_centrality(G, weight=None, dtype=float, solver="lu"): """Compute current-flow closeness centrality for nodes. Current-flow closeness centrality is variant of closeness centrality based on effective resistance between nodes in a network. This metric is also known as information centrality. Parameters ---------- G : graph A NetworkX graph. weight : None or string, optional (default=None) If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight. The weight reflects the capacity or the strength of the edge. dtype: data type (default=float) Default data type for internal matrices. Set to np.float32 for lower memory consumption. solver: string (default='lu') Type of linear solver to use for computing the flow matrix. Options are "full" (uses most memory), "lu" (recommended), and "cg" (uses least memory). Returns ------- nodes : dictionary Dictionary of nodes with current flow closeness centrality as the value. See Also -------- closeness_centrality Notes ----- The algorithm is from Brandes [1]_. See also [2]_ for the original definition of information centrality. References ---------- .. [1] Ulrik Brandes and Daniel Fleischer, Centrality Measures Based on Current Flow. Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS '05). LNCS 3404, pp. 533-544. Springer-Verlag, 2005. .. [2] Karen Stephenson and Marvin Zelen: Rethinking centrality: Methods and examples. Social Networks 11(1):1-37, 1989. """ if not nx.is_connected(G): raise nx.NetworkXError("Graph not connected.") solvername = { "full": FullInverseLaplacian, "lu": SuperLUInverseLaplacian, "cg": CGInverseLaplacian, } N = G.number_of_nodes() ordering = list(reverse_cuthill_mckee_ordering(G)) # make a copy with integer labels according to rcm ordering # this could be done without a copy if we really wanted to H = nx.relabel_nodes(G, dict(zip(ordering, range(N)))) betweenness = dict.fromkeys(H, 0.0) # b[n]=0 for n in H N = H.number_of_nodes() L = nx.laplacian_matrix(H, nodelist=range(N), weight=weight).asformat("csc") L = L.astype(dtype) C2 = solvername[solver](L, width=1, dtype=dtype) # initialize solver for v in H: col = C2.get_row(v) for w in H: betweenness[v] += col.item(v) - 2 * col.item(w) betweenness[w] += col.item(v) return {ordering[node]: 1 / value for node, value in betweenness.items()}
information_centrality = current_flow_closeness_centrality