Evolving Centralities in Temporal Graphs: A Twitter Network Analysis

Abstract

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.

Social network analysis: An overview

“…Another variation is to define temporal networks with edges that are not active over a set of times but rather over a set of intervals e = (u, v, t init , t end ). These are the interval graphs (Holme & Saramaki, 2012), good for modeling follow/unfollow relationships in Twitter network (Pereira, Amo, & Gama, 2016) or infrastructural systems like the Internet. In fact, interval graphs can be transformed into contact sequence graphs and most of the network analysis techniques hold in both cases.…”

On analyzing user preference dynamics with temporal social networks

“…The literature based on temporal networks (Holme and Saramaki 2012), focused on social media (Holme 2014), is essentially concentrated on understanding patterns of information diffusion by identifying key mediators and how temporal and topological structure of inter-action affects spreading processes. The research in Pereira et al (2016a); Wu et al (2014) discusses the various concepts of shortest path for temporal graphs and proposes efficient algorithms to compute them. In Nicosia et al (2013) graph metrics are revisited for temporal networks in order to take into account the effects of time ordering on causality.…”

“…We explore two different representations of social networks: as a static network and as a temporal network (Holme and Saramaki 2012;Pereira et al 2016a). The static network structure is a traditional approach where temporal aspects are negligible and its evolution is analyzed just as a set of graphs snapshots over time (Pereira et al 2016a). On the other hand, in temporal networks the information of when interactions between nodes happen is taken into account.…”

“…This implies in different values for the same centrality metric. The problem of evolving centralities in temporal networks is addressed in Pereira et al (2016a). Basically, in static scenarios node centrality metrics like closeness and betweenness (Zafarani et al 2014) are computed considering the concept of shortest paths on graphs.…”

“…Computing centrality values On line 6 we update node centralities values in function of the new incoming edge. We follow the greedy strategy described in Pereira et al (2016a) when computing temporal centralities or static centralities, depending on the network representation being considered. Summarizing values Each change-point scoring function requires different statistics summarized in memory.…”