### view env/lib/python3.9/site-packages/networkx/algorithms/assortativity/neighbor_degree.py @ 0:4f3585e2f14bdraftdefaulttip

author shellac Mon, 22 Mar 2021 18:12:50 +0000
line wrap: on
line source

__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 _,

.. 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.

--------
average_degree_connectivity

References
----------
..  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__