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#-*- coding: utf-8 -*-
# Copyright (C) 2011 by
# Jordi Torrents <jtorrents@milnou.net>
# Aric Hagberg <hagberg@lanl.gov>
# All rights reserved.
# BSD license.
from collections import defaultdict
import networkx as nx
__author__ = """\n""".join(['Jordi Torrents <jtorrents@milnou.net>',
'Aric Hagberg (hagberg@lanl.gov)'])
__all__ = ['average_degree_connectivity',
'k_nearest_neighbors']
def _avg_deg_conn(G, neighbors, source_degree, target_degree,
nodes=None, weight=None):
# "k nearest neighbors, or neighbor_connectivity
dsum = defaultdict(float)
dnorm = defaultdict(float)
for n,k in source_degree(nodes).items():
nbrdeg = target_degree(neighbors(n))
if weight is None:
s = float(sum(nbrdeg.values()))
else: # weight nbr degree by weight of (n,nbr) edge
s = float(sum((G[n][nbr].get(weight,1)*d
for nbr,d in nbrdeg.items())))
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
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.
Examples
--------
>>> G=nx.path_graph(4)
>>> G.edge[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'.
References
----------
.. [1] A. Barrat, M. Barthélemy, R. Pastor-Satorras, and A. Vespignani,
"The architecture of complex weighted networks".
PNAS 101 (11): 3747–3752 (2004).
"""
source_degree = G.degree
target_degree = G.degree
neighbors = G.neighbors
if G.is_directed():
direction = {'out':G.out_degree,
'in':G.in_degree,
'in+out': G.degree}
source_degree = direction[source]
target_degree = direction[target]
if source == 'in':
neighbors=G.predecessors
elif source == 'out':
neighbors=G.successors
return _avg_deg_conn(G, neighbors, source_degree, target_degree,
nodes=nodes, weight=weight)
k_nearest_neighbors=average_degree_connectivity
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