Tie-decay networks in continuous time and eigenvector-based centralities

TL;DR

This paper introduces a continuous-time network analysis framework that models evolving relationships as ties with decay, adapting PageRank centrality for such networks and demonstrating its application on social media data.

Contribution

It proposes a novel tie-decay network formalism for continuous-time systems and adapts PageRank centrality within this framework, enabling efficient analysis of dynamic networks.

Findings

Successfully adapted PageRank to tie-decay networks

Applied the method to synthetic and real-world data

Provided guidance for extending network tools to continuous-time data

Abstract

Network theory is a useful framework for studying interconnected systems of interacting entities. Many networked systems evolve continuously in time, but most existing methods for the analysis of time-dependent networks rely on discrete or discretized time. In this paper, we propose an approach for studying networks that evolve in continuous time by distinguishing between \emph{interactions}, which we model as discrete contacts, and \emph{ties}, which encode the strengths of relationships as functions of time. To illustrate our tie-decay network formalism, we adapt the well-known PageRank centrality score to our tie-decay framework in a mathematically tractable and computationally efficient way. We apply this framework to a synthetic example and then use it to study a network of retweets during the 2012 National Health Service controversy in the United Kingdom. Our work also provides guidance for similar generalizations of other tools from network theory to continuous-time networks with tie decay, including for applications to streaming data.