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.