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Table 2 Centrality measures used in this study

From: How to identify essential genes from molecular networks?

Centrality Formula Description
In degree Cu = kin(u) Number of connections into node u
Out degree Cu = kout(u) Number of connections out from node u
Sphere degree Cu = kout(u) + ∑w∩u kout(w); w is any neighbor of u. Number of nodes at 1 or 2 connections from node u
Clustering coefficient The fraction of connections between the neighbors of node u
1/Clustering coefficient  
Eccentricity Cu = max{dist(u, w): w V} The distance between node u and the most distant node in the net.
1/Eccentricity Cu = 1/max{dist(u, w): w V}  
Average distance Average distance of node u to the rest of nodes in the net
Closeness Inverse of average distance
Katz A node has a larger ckatz value while more paths reach it.
KatzR A node has a larger ckatz value while more paths leave the node.
PageRank cPR = d P cPR + ((1 - d) 1) The centrality of a node depends on its incoming connections and the relative connectivity of these connections
PageRankR cPR = d PT cPR + ((1 - d) 1) The centrality of a node depends on its outcoming connections and the relative connectivity of these connections
Integration The easiness of reaching node u from any other node
Radiality The easiness of reaching any node from node u
SP-betweenness The fraction of shortest paths inside the network, which utilize node u
  1. In the table, kin(u), kout(u) and ktot(u) refer to the incoming, outgoing and total number of edges of node u. diamG refers to the diameter of the graph and dist(u, v) stands for the distance between nodes u and v. In clustering coefficient, |e| stands for the observed paths between the neighbours of a node. In Katz A is the adjacency matrix and α a damping factor. In PageRank d is a damping factor and P the transition matrix. In the formula for shortest path (SP) betweenness σG denotes the number of shortest path from s to t. For a more detailed description of these centralities, please read [17].