Source-linked AI summary
Entropy Rate of Diffusion Processes on Complex Networks
Jesus Gomez-Gardenes, Vito Latora
TL;DR
The paper asks how diffusion dynamics and network structure jointly determine entropy rate, and introduces degree-biased random walks as a framework for studying that relationship. Analytical and numerical results show that degree heterogeneity and correlations shape entropy, while tuning the bias can maximize it for a given network topology.
Problem
Understanding diffusion in complex networks requires relating the properties of the diffusion process to the structure of the underlying network.
Method
The paper associates an entropy rate with ergodic Markov-chain diffusion processes, studying random walks whose transition probabilities are biased by neighboring node degrees and comparing real networks with degree-preserving randomized versions.
Results
The entropy rate depends on both diffusion bias and network topology, with the bias maximizing entropy differing across network structures and degree correlations.
Takeaways & Limitations
Bias tuning can maximize entropy on a given topology, with applications to data search, information dissemination, and virus or antivirus spreading in computer networks.
Takeaways & Limitations
The Markov-chain dynamics are treated on connected undirected networks, for which ergodicity and a unique stationary distribution are assured.
Abstract
from arXiv · showhide
The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree heterogeneity and correlations affect the diffusion entropy rate. In addition, the entropy rate is used to characterize complex networks from the real world. Our results point out how to design optimal diffusion processes that maximize the entropy for a given network structure, providing a new theoretical tool with applications to social, technological and communication networks.