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 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.edge[0][1]['weight'] = 5
>>> G.edge[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()
>>> G.add_path([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.