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 [R143],
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 nodes: list or iterable (optional) :
weighted: bool (default=False) :
|
---|---|
Returns : | d: dict :
|
Notes
For directed graphs you can also specify in-degree or out-degree by calling the relevant functions.
References
[R143] | (1, 2) 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.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, weighted=True)
{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_in_degree(G)
{0: 1.0, 1: 1.0, 2: 1.0, 3: 0.0}
>>> nx.average_neighbor_out_degree(G)
{0: 1.0, 1: 1.0, 2: 0.0, 3: 0.0}