Network diffusion capacity unveiled by dynamical paths

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.

References in corpus (14)

• Diffusion dynamics on multiplex networks
• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates
• Entropy Rate of Diffusion Processes on Complex Networks
• Topology-driven instabilities: the theory of pattern formation on directed networks
• Synchronization in networks with multiple interaction layers
• Pattern formation in multiplex networks
• Turing patterns in multiplex networks
• Laplacian Renormalization Group for heterogeneous networks
• Low-dimensional behavior of Kuramoto model with inertia in complex networks
• Diffusive behavior of multiplex networks
• Functional Control of Oscillator Networks
• Network diffusion capacity unveiled by dynamical paths
• Self-organized explosive synchronization in complex networks: Emergence of synchronization bombs

Cited by in corpus (2)

• Network diffusion capacity unveiled by dynamical paths
• Understanding How Network Geometry Influences Diffusion Processes in Complex Networks: A Focus on Cryptocurrency Blockchains and Critical Infrastructure Networks