# Source code for networkx.algorithms.assortativity.connectivity

from collections import defaultdict

import networkx as nx

__all__ = ["average_degree_connectivity"]

[docs]
@nx._dispatchable(edge_attrs="weight")
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
------
NetworkXError
If either source or target are not one of 'in',
'out', or 'in+out'.
If either source or target is passed for an undirected graph.

Examples
--------
>>> G = nx.path_graph(4)
>>> G.edges[1, 2]["weight"] = 3
>>> nx.average_degree_connectivity(G)
{1: 2.0, 2: 1.5}
>>> nx.average_degree_connectivity(G, weight="weight")
{1: 2.0, 2: 1.75}

--------
average_neighbor_degree

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 nx.NetworkXError('source must be one of "in", "out", or "in+out"')
if target not in ("in", "out", "in+out"):
raise nx.NetworkXError('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:
if source != "in+out" or target != "in+out":
raise nx.NetworkXError(
f"source and target arguments are only supported for directed graphs"
)
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
return {k: avg if dnorm[k] == 0 else avg / dnorm[k] for k, avg in dsum.items()}