average_degree_connectivity

average_degree_connectivity(G, source='in+out', target='in+out', nodes=None, weight=None)

Compute the average degree connectivity of graph.

The average degree connectivity is the average nearest neighbor degree of nodes with degree k. For weighted graphs, an analogous measure can be computed using the weighted average neighbors degree defined in [1], for a node i, as

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

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

source“in”|”out”|”in+out” (default:”in+out”)

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

target“in”|”out”|”in+out” (default:”in+out”

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

nodeslist or iterable (optional)

Compute neighbor connectivity for these nodes. The default is all nodes.

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:

ddict

A dictionary keyed by degree k with the value of average connectivity.

Raises:

NetworkXError

If either source or target are not one of ‘in’, ‘out’, or ‘in+out’. If either source or target is passed for an undirected graph.

See also

average_neighbor_degree

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[1, 2]["weight"] = 3
>>> nx.average_degree_connectivity(G)
{1: 2.0, 2: 1.5}
>>> nx.average_degree_connectivity(G, weight="weight")
{1: 2.0, 2: 1.75}