Self-loops in Social Networks: Behavior of Eigenvector Centrality

Centrality measures are an essential tool in understanding complex networks, since they give researcher insights on the role the different nodes/actors play in them. Among them, eigenvector centrality is a principled approach to these measures, using a mathematical operation on the connection matrix. This connection matrix includes connections from an actor to itself (the diagonal); however, as it is the case with most centrality measures, this fact is seldom used in social studies to compute the standing or influence of one node over others. In this paper we will analyze the difference in EV centrality with or without these self connections or self-loops and how the change depends on the actual number of these self-loops or the weight of these self-connections. Finally, we will characterize in which cases, if any, it is effective to drop self-loops and what kind of information it will give us on the nature and dynamics of the network.