# 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 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],

$k_{nn,i}^{w} = \frac{1}{s_i} \sum_{j \in N(i)} w_{ij} k_j$

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
GNetworkX graph
sourcestring (“in”|”out”|”in+out”)

Directed graphs only. Use “in”- or “out”-degree for source node.

targetstring (“in”|”out”|”in+out”)

Directed graphs only. Use “in”- or “out”-degree for target node.

nodeslist or iterable, optional

Compute neighbor degree for specified nodes. The default is all nodes in the graph.

weightstring 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.

Notes

For directed graphs you can also specify in-degree or out-degree by passing keyword arguments.

References

1

A. Barrat, M. Barthélemy, R. Pastor-Satorras, and A. Vespignani, “The architecture of complex weighted networks”. PNAS 101 (11): 3747–3752 (2004).

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: 0.0, 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}