Causality-Driven Slow-Down and Speed-Up of Diffusion in Non-Markovian Temporal Networks

TL;DR

This paper introduces an analytical methodology to predict how non-Markovian temporal network properties influence the speed of diffusion processes, revealing that such properties can either slow down or speed up diffusion beyond static network effects.

Contribution

The authors develop a novel analytical approach to quantify causality-driven diffusion speed changes in non-Markovian temporal networks, validated across six real-world datasets.

Findings

Non-Markovian characteristics can significantly alter diffusion speed.

Diffusion can be either slowed down or sped up due to non-Markovian effects.

These effects can outweigh the influence of static community structures.

Abstract

Recent research has highlighted limitations of studying complex systems with time-varying topologies from the perspective of static, time-aggregated networks. Non-Markovian characteristics resulting from the ordering of interactions in temporal networks were identified as one important mechanism that alters causality, and affects dynamical processes. So far, an analytical explanation for this phenomenon and for the significant variations observed across different systems is missing. Here we introduce a methodology that allows to analytically predict causality-driven changes of diffusion speed in non-Markovian temporal networks. Validating our predictions in six data sets, we show that - compared to the time-aggregated network - non-Markovian characteristics can lead to both a slow-down, or speed-up of diffusion which can even outweigh the decelerating effect of community structures in the static topology. Thus, non-Markovian properties of temporal networks constitute an important additional dimension of complexity in time-varying complex systems.