133 lines
4.2 KiB
Python
133 lines
4.2 KiB
Python
#-*- 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
|
||
|
||
|
||
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 neighborhood 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.edges[0, 1]['weight'] = 5
|
||
>>> G.edges[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__
|