#-*- coding: utf-8 -*-
# Copyright (C) 2011 by
# Jordi Torrents <jtorrents@milnou.net>
# Aric Hagberg <hagberg@lanl.gov>
# All rights reserved.
# BSD license.
import networkx as nx
__author__ = """\n""".join(['Jordi Torrents <jtorrents@milnou.net>',
'Aric Hagberg (hagberg@lanl.gov)'])
__all__ = ["average_neighbor_degree"]
def _average_nbr_deg(G, source_degree, target_degree, nodes=None, weight=None):
# average degree of neighbors
avg = {}
for n,deg in source_degree(nodes,weight=weight):
# normalize but not by zero degree
if deg == 0:
deg = 1
nbrdeg = target_degree(G[n])
if weight is None:
avg[n] = sum(d for n, d in nbrdeg) / float(deg)
else:
avg[n] = sum((G[n][nbr].get(weight,1)*d
for nbr,d in nbrdeg)) / float(deg)
return avg
[docs]def average_neighbor_degree(G, source='out', target='out',
nodes=None, weight=None):
r"""Returns the average degree of the neighborhood of each node.
The average degree of a node `i` is
.. math::
k_{nn,i} = \frac{1}{|N(i)|} \sum_{j \in N(i)} k_j
where `N(i)` are the neighbors of node `i` and `k_j` is
the degree of node `j` which belongs to `N(i)`. For weighted
graphs, an analogous measure can be defined [1]_,
.. 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 : string ("in"|"out")
Directed graphs only.
Use "in"- or "out"-degree for source node.
target : string ("in"|"out")
Directed graphs only.
Use "in"- or "out"-degree for target node.
nodes : list or iterable, optional
Compute neighbor degree for specified nodes. The default is
all nodes in the graph.
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 node with average neighbors degree value.
Examples
--------
>>> G=nx.path_graph(4)
>>> G.edge[0][1]['weight'] = 5
>>> G.edge[2][3]['weight'] = 3
>>> nx.average_neighbor_degree(G)
{0: 2.0, 1: 1.5, 2: 1.5, 3: 2.0}
>>> nx.average_neighbor_degree(G, weight='weight')
{0: 2.0, 1: 1.1666666666666667, 2: 1.25, 3: 2.0}
>>> G=nx.DiGraph()
>>> nx.add_path(G, [0, 1, 2, 3])
>>> nx.average_neighbor_degree(G, source='in', target='in')
{0: 1.0, 1: 1.0, 2: 1.0, 3: 0.0}
>>> nx.average_neighbor_degree(G, source='out', target='out')
{0: 1.0, 1: 1.0, 2: 0.0, 3: 0.0}
Notes
-----
For directed graphs you can also specify in-degree or out-degree
by passing keyword arguments.
See Also
--------
average_degree_connectivity
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
if G.is_directed():
direction = {'out':G.out_degree,
'in':G.in_degree}
source_degree = direction[source]
target_degree = direction[target]
return _average_nbr_deg(G, source_degree, target_degree,
nodes=nodes, weight=weight)
# obsolete
# def average_neighbor_in_degree(G, nodes=None, weight=None):
# if not G.is_directed():
# raise nx.NetworkXError("Not defined for undirected graphs.")
# return _average_nbr_deg(G, G.in_degree, G.in_degree, nodes, weight)
# average_neighbor_in_degree.__doc__=average_neighbor_degree.__doc__
# def average_neighbor_out_degree(G, nodes=None, weight=None):
# if not G.is_directed():
# raise nx.NetworkXError("Not defined for undirected graphs.")
# return _average_nbr_deg(G, G.out_degree, G.out_degree, nodes, weight)
# average_neighbor_out_degree.__doc__=average_neighbor_degree.__doc__