Effect of Memory on the Dynamics of Random Walks on Networks

Research output: Contribution to journalArticlepeer-review


Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second- order Markov models, and derive an analytical expression for the effect of memory on the spectral gap and thus, equivalently, on the characteristic time needed for the stochastic process to asymptotically reach equilibrium. Perturbation analysis shows that standard first-order Markov models can either overestimate or underestimate the diffusion rate of flows across the modular structure of a system captured by a second- order Markov network. We test the theoretical predictions on a toy example and on numerical data, and discuss their implications for network theory, in particular in the case of temporal or multiplex networks.
Original languageEnglish
JournalJournal of Complex Networks
Publication statusPublished - 30 Jun 2014


  • random walks; spectral gap; non-Markovian process; temporal networks.


Dive into the research topics of 'Effect of Memory on the Dynamics of Random Walks on Networks'. Together they form a unique fingerprint.

Cite this