networkx.algorithms.structuralholes.local_constraint¶

local_constraint(G, u, v, weight=None)[source]¶

Returns the local constraint on the node u with respect to the node v in the graph G.

Formally, the local constraint on u with respect to v, denoted $\ell(v)$ , is defined by

$\ell(u, v) = \left(p_{uv} + \sum_{w \in N(v)} p_{uw} p{wv}\right)^2,$

where $N(v)$ is the set of neighbors of $v$ and $p_{uv}$ is the normalized mutual weight of the (directed or undirected) edges joining $u$ and $v$ , for each vertex $u$ and $v$ [1]. The mutual weight of $u$ and $v$ is the sum of the weights of edges joining them (edge weights are assumed to be one if the graph is unweighted).

Parameters:	G (NetworkX graph) – The graph containing `u` and `v`. This can be either directed or undirected. u (node) – A node in the graph `G`. v (node) – A node in the graph `G`. weight (None or string, optional) – If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight.
Returns:	The constraint of the node `v` in the graph `G`.
Return type:	float