Optimal Intervention on Weighted Networks via Edge Centrality

Dongyue Li, Tina Eliassi-Rad, Hongyang R. Zhang

Keywords: Targeted Immunization, Graph Algorithms, Epidemic Spreading, Edge Centrality.

Abstract:

We consider the problem of diffusion control via interventions that change network topologies. We study this problem for general weighted networks and present an iterative algorithm, Frank-Wolfe-EdgeCentrality, to reduce the spread of a diffusion process by shrinking the network's top singular values. Given an edge-weight reduction budget, our algorithm identifies the near-optimal edge-weight reduction strategy to minimize the sum of the largest $r$ eigenvalues of $W^{\top}W$, where $W$ is the network weight matrix. Our algorithm provably converges to the optimum at a rate of $O(t^{-1})$ after $t$ iterations; each iteration only requires a nearly-linear runtime in the number of edges.

We perform a detailed empirical study of our algorithm on a wide range of weighted networks. In particular, we apply our approach to reduce edge weights on mobility networks (between points of interest and census block groups), which have been used to model the spread of COVID-19. In SEIR model simulations, our algorithm reduces the number of infections by 25.70% more than existing approaches, averaged over three weighted graphs and eight mobility networks. Meanwhile, the largest singular value of the weight matrix $W$ decreases by 25.48% more than existing approaches on these networks. An extension of our algorithm to temporal mobility networks also shows an effective reduction in the number of infected nodes.

TL;DR: We design an iterative edge centrality minimization algorithm to reduce the top eigenvalue of weighted networks and epidemic spreading.