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:
  • 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:

dict

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.

References

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