Dynamic topologies of activity-driven temporal networks with memory
Hyewon Kim, Meesoon Ha, and Hawoong Jeong

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…
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