networkx.algorithms.assortativity.average_neighbor_degree¶

average_neighbor_degree
(G, source='out', target='out', nodes=None, weight=None)[source]¶ Returns the average degree of the neighborhood of each node.
The average neighborhood degree of a node
i
is\[k_{nn,i} = \frac{1}{N(i)} \sum_{j \in N(i)} k_j\]where
N(i)
are the neighbors of nodei
andk_j
is the degree of nodej
which belongs toN(i)
. For weighted graphs, an analogous measure can be defined 1,\[k_{nn,i}^{w} = \frac{1}{s_i} \sum_{j \in N(i)} w_{ij} k_j\]where
s_i
is the weighted degree of nodei
,w_{ij}
is the weight of the edge that linksi
andj
andN(i)
are the neighbors of nodei
. 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 – A dictionary keyed by node with average neighbors degree value.
 Return type
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 indegree or outdegree by passing keyword arguments.
See also
References
 1
A. Barrat, M. Barthélemy, R. PastorSatorras, and A. Vespignani, “The architecture of complex weighted networks”. PNAS 101 (11): 3747–3752 (2004).