Optimal networks for dynamical spreading

TL;DR

This paper develops an analytic framework to identify optimal network structures for SIS epidemic spreading, revealing how optimal degree distributions vary with infection rates and uncovering a unique infection rate where all networks are equally effective.

Contribution

It introduces a novel analytic approach to solve the inverse problem for SIS dynamics on annealed networks, characterizing optimal degree distributions across different infection regimes.

Findings

Optimal degree distribution is unique at low/high infection rates.

Intermediate infection rates lead to diverse optimal degree distributions.

A specific infection rate exists where all degree distributions are equally optimal.

Abstract

The inverse problem of finding the optimal network structure for a specific type of dynamical process stands out as one of the most challenging problems in network science. Focusing on the susceptible-infected-susceptible type of dynamics on annealed networks whose structures are fully characterized by the degree distribution, we develop an analytic framework to solve the inverse problem. We find that, for relatively low or high infection rates, the optimal degree distribution is unique, which consists of no more than two distinct nodal degrees. For intermediate infection rates, the optimal degree distribution is multitudinous and can have a broader support. We also find that, in general, the heterogeneity of the optimal networks decreases with the infection rate. A surprising phenomenon is the existence of a specific value of the infection rate for which any degree distribution would be optimal in generating maximum spreading prevalence. The analytic framework and the findings provide insights into the interplay between network structure and dynamical processes with practical implications.