Tiedecay networks in continuous time and eigenvectorbased centralities
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 timedependent 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 tiedecay network formalism, we adapt the wellknown PageRank centrality score to our tiedecay 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 continuoustime networks with tie decay, including for applications to streaming data.
 Publication:

arXiv eprints
 Pub Date:
 May 2018
 arXiv:
 arXiv:1805.00193
 Bibcode:
 2018arXiv180500193A
 Keywords:

 Physics  Physics and Society;
 Computer Science  Social and Information Networks;
 Mathematics  Numerical Analysis;
 Mathematics  Probability;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems