Dynamic topologies of activity-driven temporal networks with memory

TL;DR

This paper investigates how memory and time resolution influence the evolving structure and diffusion processes in activity-driven temporal networks, revealing memory-dependent scaling behaviors and proposing a finite-size scaling framework.

Contribution

It introduces a comprehensive model incorporating memory into activity-driven temporal networks and analyzes the effects on topology and diffusion, extending understanding of dynamic network behavior.

Findings

Memory affects the scaling properties of the largest cluster.

Time resolution determines the effective network size.

Memory influences the transition from dynamic to static regimes.

Abstract

We propose dynamic scaling in temporal networks with heterogeneous activities and memory, and provide a comprehensive picture for the dynamic topologies of such networks, in terms of the modified activity-driven network model [H. Kim \textit{et al.}, Eur. Phys. J. B {\bf 88}, 315 (2015)]. Particularly, we focus on the interplay of the time resolution and memory in dynamic topologies. Through the random walk (RW) process, we investigate diffusion properties and topological changes as the time resolution increases. Our results with memory are compared to those of the memoryless case. Based on the temporal percolation concept, we derive scaling exponents in the dynamics of the largest cluster and the coverage of the RW process in time-varying networks. We find that the time resolution in the time-accumulated network determines the effective size of the network, while memory affects relevant scaling properties at the crossover from the dynamic regime to the static one. The origin of memory-dependent scaling behaviors is the dynamics of the largest cluster, which depends on temporal degree distributions. Finally, we conjecture of the extended finite-size scaling ansatz for dynamic topologies and the fundamental property of temporal networks, which are numerically confirmed.