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.