Source code for networkx.algorithms.centrality.dispersion

from itertools import combinations

import networkx as nx

__all__ = ["dispersion"]

[docs] @nx._dispatchable def dispersion(G, u=None, v=None, normalized=True, alpha=1.0, b=0.0, c=0.0): r"""Calculate dispersion between `u` and `v` in `G`. A link between two actors (`u` and `v`) has a high dispersion when their mutual ties (`s` and `t`) are not well connected with each other. Parameters ---------- G : graph A NetworkX graph. u : node, optional The source for the dispersion score (e.g. ego node of the network). v : node, optional The target of the dispersion score if specified. normalized : bool If True (default) normalize by the embeddedness of the nodes (u and v). alpha, b, c : float Parameters for the normalization procedure. When `normalized` is True, the dispersion value is normalized by:: result = ((dispersion + b) ** alpha) / (embeddedness + c) as long as the denominator is nonzero. Returns ------- nodes : dictionary If u (v) is specified, returns a dictionary of nodes with dispersion score for all "target" ("source") nodes. If neither u nor v is specified, returns a dictionary of dictionaries for all nodes 'u' in the graph with a dispersion score for each node 'v'. Notes ----- This implementation follows Lars Backstrom and Jon Kleinberg [1]_. Typical usage would be to run dispersion on the ego network $G_u$ if $u$ were specified. Running :func:`dispersion` with neither $u$ nor $v$ specified can take some time to complete. References ---------- .. [1] Romantic Partnerships and the Dispersion of Social Ties: A Network Analysis of Relationship Status on Facebook. Lars Backstrom, Jon Kleinberg. """ def _dispersion(G_u, u, v): """dispersion for all nodes 'v' in a ego network G_u of node 'u'""" u_nbrs = set(G_u[u]) ST = {n for n in G_u[v] if n in u_nbrs} set_uv = {u, v} # all possible ties of connections that u and b share possib = combinations(ST, 2) total = 0 for s, t in possib: # neighbors of s that are in G_u, not including u and v nbrs_s = u_nbrs.intersection(G_u[s]) - set_uv # s and t are not directly connected if t not in nbrs_s: # s and t do not share a connection if nbrs_s.isdisjoint(G_u[t]): # tick for disp(u, v) total += 1 # neighbors that u and v share embeddedness = len(ST) dispersion_val = total if normalized: dispersion_val = (total + b) ** alpha if embeddedness + c != 0: dispersion_val /= embeddedness + c return dispersion_val if u is None: # v and u are not specified if v is None: results = {n: {} for n in G} for u in G: for v in G[u]: results[u][v] = _dispersion(G, u, v) # u is not specified, but v is else: results = dict.fromkeys(G[v], {}) for u in G[v]: results[u] = _dispersion(G, v, u) else: # u is specified with no target v if v is None: results = dict.fromkeys(G[u], {}) for v in G[u]: results[v] = _dispersion(G, u, v) # both u and v are specified else: results = _dispersion(G, u, v) return results