Centrality Fairness: Measuring and Analyzing Structural Inequality of Online Social Network

Abstract

While measuring inequality of a social system has been a popular topic in economics and sociology, structural fairness and inequality of social networks has not been paid attention by researchers interested in web or social network analysis. In practice, measuring structural fairness and inequality has a number of applications in online social networks, for example, we can check skewness of degree distribution by simply seeing inequality index. The powerlaw exponent has often been used to measure the inequality of network structures, however, it has several drawbacks to be applied to universal networks. In this paper, we propose a novel framework to measure fairness and inequality of a given network in the context of its structure. We develop a set of centrality fairness measures by combining other well-known node centralities with Gini index. We also analyze scale-free property of our proposed centrality fairness measures in real networks. Moreover, we suggest simple and efficient methods to relax structural inequality of a network, which are based on two edge manipulations: addition and rotation. Through experiments on real networks, we show that our methods decrease inequality quite steadily and effectively, and as structural hierarchy of a network gets stronger, decreasing rate of inequality gets lower.