# 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:
GNetworkX graph

The graph containing u and v. This can be either directed or undirected.

unode

A node in the graph G.

vnode

A node in the graph G.

weightNone or string, optional

If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight.

Returns:
float

The constraint of the node v in the graph G.

References

[1]

Burt, Ronald S. “Structural holes and good ideas”. American Journal of Sociology (110): 349–399.