Network diffusion capacity unveiled by dynamical paths

TL;DR

This paper introduces the diffusion capacity measure to quantify and predict the potential of networks to propagate information, considering both structural topology and dynamical processes, demonstrated through heat and SIR models.

Contribution

The paper proposes a novel measure called diffusion capacity that captures the interplay of network structure and dynamics to evaluate and predict diffusion performance.

Findings

Diffusion capacity effectively predicts spreading evolution in SIR models.

The measure helps identify structural modifications to enhance diffusion.

Application to heat and SIR models demonstrates broad utility.

Abstract

Improving the understanding of diffusive processes in networks with complex topologies is one of the main challenges of today's complexity science. Each network possesses an intrinsic diffusive potential that depends on its structural connectivity. However, the diffusion of a process depends not only on this topological potential but also on the dynamical process itself. Quantifying this potential will allow the design of more efficient systems in which it is necessary either to weaken or to enhance diffusion. Here we introduce a measure, the {\em diffusion capacity}, that quantifies, through the concept of dynamical paths, the potential of an element of the system, and also, of the system itself, to propagate information. Among other examples, we study a heat diffusion model and SIR model to demonstrate the value of the proposed measure. We found, in the last case, that diffusion capacity can be used as a predictor of the evolution of the spreading process. In general, we show that the diffusion capacity provides an efficient tool to evaluate the performance of systems, and also, to identify and quantify structural modifications that could improve diffusion mechanisms.