Topological clustering of multilayer networks

Significance Multilayer network clustering is used in such diverse areas as optimal islanding of critical infrastructures, analysis of trade agreements, and monitoring ecological interaction patterns. We propose a perspective on multilayer network clustering based on the concept of shape. By invoking the machinery of topological data analysis, we first study a shape of each node neighborhood and then group nodes based on how similar shapes of their local neighborhoods are. The significance of this methodology can be viewed through an emerging problem of sustainability of house insurance to climate risks. The topological perspective opens possibilities for more systematic, robust, and mathematically rigorous integration of higher-order network properties and their interplay to the analysis of complex networks.