Solvable non-Markovian dynamic network

TL;DR

This paper introduces an analytically solvable non-Markovian dynamic network model with heavy-tailed inter-event times, demonstrating its effectiveness in approximating power-law network dynamics and coupled spreading processes.

Contribution

It develops a tractable system of equations for non-Markovian networks with Mittag-Leffler distributed inter-event times, bridging theory and simulation.

Findings

Excellent agreement between Mittag-Leffler model and power-law inter-event time simulations.

Model accurately captures coupled SIS spreading dynamics.

Provides a foundation for analyzing complex non-Markovian networks.

Abstract

Non-Markovian processes are widespread in natural and human-made systems, yet explicit model- ling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy tailed Mittag-Leffler distribution for the inter-event times. We derive an analytically and computationally tractable system of Kolmogorov- like forward equations utilising the Caputo derivative for the probability of having a given number of active links in the network and solve them. Simulations for the RLAD are also studied for power-law inter-event times and we show excellent agreement with the Mittag-Leffler model. This agreement holds even when the RLAD network dynamics is coupled with the susceptible-infected-susceptible (SIS) spreading dynamics. Thus, the analytically solvable Mittag-Leffler model provides an excel- lent approximation to the case when the network dynamics is characterised by power-law distributed inter-event times. We further discuss possible generalizations of our result.