Evolving Centralities in Temporal Graphs: A Twitter Network Analysis

In online social media systems users are not only posting, consuming, and sharing content, but also creating new and destroying existing connections in the underlying social network. This behavior lead us to investigate how user structural position reacts with the evolution of the underlying social network structure. While centrality metrics have been studied in the past, much less is known about their temporal behaviors and processing, mainly when analyzing not just networks snapshots, but interval graphs. Here, we study Twitter follower/followee network and how users centralities evolve over time. Our analysis is founded on temporal graphs theory. First, we model Twitter as a temporal network and revisit the concept of shortest path considering the time dimension. We show how to compute closeness and betweenness centralities using fastest paths. Then, we propose a baseline algorithm for mining streams of temporal networks. The task is to find all pairs fastest paths inside an observation window. We find that Twitter users are fairly dynamic and from one moment to the next, they can assume (or leave) central roles in the network.