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 $ℓ (v)$ , is defined by

ℓ (u, v) = {(p_{u v} + \sum_{w \in N (v)} p_{u w} p_{w v})}^{2},

where $N (v)$ is the set of neighbors of $v$ and $p_{u v}$ 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.