Aging and percolation dynamics in a Non-Poissonian temporal network model

TL;DR

This paper provides a detailed mathematical analysis of the NoPAD model, revealing how aging effects influence the topology and percolation properties of temporal networks with bursty social interactions.

Contribution

It offers the first comprehensive analytical study of aging effects on degree distribution and percolation thresholds in the NoPAD temporal network model.

Findings

Derived explicit degree distribution formulas under aging effects

Identified how aging influences the percolation threshold

Validated analytical results with extensive simulations

Abstract

We present an exhaustive mathematical analysis of the recently proposed Non-Poissonian Ac- tivity Driven (NoPAD) model [Moinet et al. Phys. Rev. Lett., 114 (2015)], a temporal network model incorporating the empirically observed bursty nature of social interactions. We focus on the aging effects emerging from the Non-Poissonian dynamics of link activation, and on their effects on the topological properties of time-integrated networks, such as the degree distribution. Analytic expressions for the degree distribution of integrated networks as a function of time are derived, ex- ploring both limits of vanishing and strong aging. We also address the percolation process occurring on these temporal networks, by computing the threshold for the emergence of a giant connected component, highlighting the aging dependence. Our analytic predictions are checked by means of extensive numerical simulations of the NoPAD model.