Optimal information diffusion in stochastic block models

TL;DR

This paper investigates how different network structures, including assortative, core-periphery, and disassortative, influence the optimal spread of information using the linear threshold model on stochastic block models.

Contribution

It identifies the types of network structures that maximize information diffusion and minimize initial informed nodes for triggering cascades within a stochastic block model framework.

Findings

Optimal networks can be assortative, core-periphery, or disassortative.

Core-periphery structures are nearly optimal for minimal initial informed nodes.

Dense core linked to sparse periphery facilitates efficient information spread.

Abstract

We use the linear threshold model to study the diffusion of information on a network generated by the stochastic block model. We focus our analysis on a two community structure where the initial set of informed nodes lies only in one of the two communities and we look for optimal network structures, i.e. those maximizing the asymptotic extent of the diffusion. We find that, constraining the mean degree and the fraction of initially informed nodes, the optimal structure can be assortative (modular), core-periphery, or even disassortative. We then look for minimal cost structures, i.e. those such that a minimal fraction of initially informed nodes is needed to trigger a global cascade. We find that the optimal networks are assortative but with a structure very close to a core-periphery graph, i.e. a very dense community linked to a much more sparsely connected periphery.