Note

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

Source code for networkx.algorithms.assortativity.connectivity

from collections import defaultdict

__all__ = ["average_degree_connectivity", "k_nearest_neighbors"]


[docs]def average_degree_connectivity( G, source="in+out", target="in+out", nodes=None, weight=None ): r"""Compute the average degree connectivity of graph. The average degree connectivity is the average nearest neighbor degree of nodes with degree k. For weighted graphs, an analogous measure can be computed using the weighted average neighbors degree defined in [1]_, for a node `i`, as .. math:: k_{nn,i}^{w} = \frac{1}{s_i} \sum_{j \in N(i)} w_{ij} k_j where `s_i` is the weighted degree of node `i`, `w_{ij}` is the weight of the edge that links `i` and `j`, and `N(i)` are the neighbors of node `i`. Parameters ---------- G : NetworkX graph source : "in"|"out"|"in+out" (default:"in+out") Directed graphs only. Use "in"- or "out"-degree for source node. target : "in"|"out"|"in+out" (default:"in+out" Directed graphs only. Use "in"- or "out"-degree for target node. nodes : list or iterable (optional) Compute neighbor connectivity for these nodes. The default is all nodes. weight : string or None, optional (default=None) The edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. Returns ------- d : dict A dictionary keyed by degree k with the value of average connectivity. Raises ------ ValueError If either `source` or `target` are not one of 'in', 'out', or 'in+out'. Examples -------- >>> G = nx.path_graph(4) >>> G.edges[1, 2]["weight"] = 3 >>> nx.k_nearest_neighbors(G) {1: 2.0, 2: 1.5} >>> nx.k_nearest_neighbors(G, weight="weight") {1: 2.0, 2: 1.75} See also -------- neighbors_average_degree Notes ----- This algorithm is sometimes called "k nearest neighbors" and is also available as `k_nearest_neighbors`. References ---------- .. [1] A. Barrat, M. Barthélemy, R. Pastor-Satorras, and A. Vespignani, "The architecture of complex weighted networks". PNAS 101 (11): 3747–3752 (2004). """ # First, determine the type of neighbors and the type of degree to use. if G.is_directed(): if source not in ("in", "out", "in+out"): raise ValueError('source must be one of "in", "out", or "in+out"') if target not in ("in", "out", "in+out"): raise ValueError('target must be one of "in", "out", or "in+out"') direction = {"out": G.out_degree, "in": G.in_degree, "in+out": G.degree} neighbor_funcs = { "out": G.successors, "in": G.predecessors, "in+out": G.neighbors, } source_degree = direction[source] target_degree = direction[target] neighbors = neighbor_funcs[source] # `reverse` indicates whether to look at the in-edge when # computing the weight of an edge. reverse = source == "in" else: source_degree = G.degree target_degree = G.degree neighbors = G.neighbors reverse = False dsum = defaultdict(int) dnorm = defaultdict(int) # Check if `source_nodes` is actually a single node in the graph. source_nodes = source_degree(nodes) if nodes in G: source_nodes = [(nodes, source_degree(nodes))] for n, k in source_nodes: nbrdeg = target_degree(neighbors(n)) if weight is None: s = sum(d for n, d in nbrdeg) else: # weight nbr degree by weight of (n,nbr) edge if reverse: s = sum(G[nbr][n].get(weight, 1) * d for nbr, d in nbrdeg) else: s = sum(G[n][nbr].get(weight, 1) * d for nbr, d in nbrdeg) dnorm[k] += source_degree(n, weight=weight) dsum[k] += s # normalize dc = {} for k, avg in dsum.items(): dc[k] = avg norm = dnorm[k] if avg > 0 and norm > 0: dc[k] /= norm return dc
k_nearest_neighbors = average_degree_connectivity