Degree Correlations Amplify the Growth of Cascades in Networks

TL;DR

This paper explores how degree correlations in networks influence the initiation and growth of cascades, revealing that positive assortativity can enhance the role of low-degree nodes in triggering large cascades.

Contribution

It introduces a new measure of degree assortativity relevant to spreading processes and demonstrates its impact on cascade dynamics and seed node selection.

Findings

Degree correlations significantly affect cascade thresholds.

Positive assortativity increases the likelihood of low-degree nodes triggering large cascades.

Manipulating network structure can tailor spreading processes.

Abstract

Networks facilitate the spread of cascades, allowing a local perturbation to percolate via interactions between nodes and their neighbors. We investigate how network structure affects the dynamics of a spreading cascade. By accounting for the joint degree distribution of a network within a generating function framework, we can quantify how degree correlations affect both the onset of global cascades and the propensity of nodes of specific degree class to trigger large cascades. However, not all degree correlations are equally important in a spreading process. We introduce a new measure of degree assortativity that accounts for correlations among nodes relevant to a spreading cascade. We show that the critical point defining the onset of global cascades has a monotone relationship to this new assortativity measure. In addition, we show that the choice of nodes to seed the largest cascades is strongly affected by degree correlations. Contrary to traditional wisdom, when degree assortativity is positive, low degree nodes are more likely to generate largest cascades. Our work suggests that it may be possible to tailor spreading processes by manipulating the higher-order structure of networks.