Login The Centiserver on OMICTools 
Knotty CentralityDefinition
A network measure called knottycentrality is defined that quantifies the extent to which a given subset of a graph’s nodes
constitutes a densely intraconnected topologically central connective core. Using this measure, the knotty centre of a
network is defined as a subgraph with maximal knottycentrality.
Consider a directed graph G with N nodes. The knottycentrality of a (nonempty, nonsingleton) subset S of the nodes in G is given by where E_{s} is the number of edges between nodes in S, and N_{s} is the number of nodes in S. bc(i) is the betweenness centrality of node i normalised with respect to the whole graph, such that where BC(i) is the (directed) betweenness centrality of node i. Knottycentrality ranges from 0 to 1. It is 0 if none of the nodes in S is adjacent (E_{s}=0): It is 1 if S is a clique and . If G is a clique then and KC(S) is undefined. The measure can be applied to either weighted or unweighted graphs by substituting weighted or unweighted variants of betweenness centrality into equation. SoftwareReferences
