Centrality metrics : including nodes’ attributes and generalizing geometric and homophily metrics in social network analysis

Abstract

Many social interactions can be modeled by networks, in which social actors are represented by nodes and their relationships by edges. Researchers over the years have used social network analysis (SNA) to study the topological structure of the network and understand relational patterns. There are several centrality measures in the literature, with different criteria that define which nodes are more central. In addition, several studies seek to understand how network structures are formed. More recently, scholars have included in the SNA the actors’ attributes in the search for a better understanding, given that these attributes can influence the way relationships occur and, consequently, affect the network structure. By exploring gaps in the literature, this PhD Dissertation aims to contribute to the advancement of this field proposing new metrics: (i) considering the geodesic paths among pairs of nodes, it is proposed a generalized measure, called p-means centrality, depending on the value given to the parameter p, several measures of centrality are obtained; (ii) two centrality measures, based on the law of gravity are proposed, in which the strength of the nodes’ attributes is combined with the strength of the relationships between them, the main measure is called energy disruptive; (iii) to explore the network formation, two measures are proposed that generalize the EI Index, a measure of homophily. One can be applied in case of disjoint and non-disjoint groups and the other, more complete, also explores the case of fuzzy groups. Several networks were considered to test the use of these metrics: (i) the p-means centrality was applied in a co-authorship network and in a transport network; (ii) disruptive energy centrality was applied in two crime networks; (iii) the two measures that generalize the EI index were applied in a co-authorship network and in an international trade network. Among the best results obtained it can be highlighted: (i) the p-means centrality have shown that the most central nodes, defined by negative values of p, are closer to the nodes with the greatest spreading capacity, defined by the Susceptible-Infectious- Recovered (SIR) model; (ii) disruptive energy centrality, when used as a target method, was the most efficient strategy, providing greater network damage than other centrality measures analyzed; (iii) the EI index was able to explore the formation of networks in cases of non-disjoint groups and also fuzzy groups, proving the generalization of the measures. Therefore, the metrics proposed in this work enhance the SNA by unifying existing centrality metrics, incorporating nodes’ attributes in SNA metrics, and extending the scope of homophily studies to more general types of groups.