A Centrality Measure for Directed Networks: m-Ranking Method

Abstract

Understanding the importance of actors (or nodes) in complex networks is an area in social network research. Importance of nodes is interpreted in different ways in different context. If the focus of research is on the spreading of information, then nodes which can spread information throughout the network in a faster pace than any other nodes is important. In the study of spread of disease or virus in a network, the nodes which are at minimum distance from all other nodes are most important. Depending upon the number of direct and indirect connections that each node has in a network, its participation in the spreading varies. Indirect connections specify the nodes that are at two steps, three steps, etc., away from a node. Research for potential spreaders in undirected networks is almost saturated. But in the study of spreading of information, directed networks are more important than undirected networks. In section two of this paper we review some widely used methods to identify important nodes in an undirected network. We also discuss methods which produce similar results for directed networks as well. Wherever necessary we make comparisons of the methods and point out advantages of one method over the other. In section three we propose a method that helps to rank the nodes in a directed network, which takes into account the relative importance of all nodes and directed edges in it.