On network analysis using non-additive integrals: extending the game-theoretic network centrality

Abstract

There are large amounts of information that can be represented in terms of graphs. This includes social networks and internet. We can represent people and their interactions by means of graphs. Similarly, we can represent web pages (and sites) as well as links between pages by means of graphs. In order to study the properties of graphs, several indices have been defined. They include degree centrality, betweenness, and closeness. In this paper, we propose the use of Choquet and Sugeno integrals with respect to non-additive measures for network analysis. This is a natural extension of the use of game theory for network analysis. Recall that monotonic games in game theory are non-additive measures. We discuss the expected force, a centrality measure, in the light of non-additive integral network analysis. We also show that some results by Godo et al. can be used to compute network indices when the information associated with a graph is qualitative.