The nestedness of higher-order networks

TL;DR

This paper reviews measures of nestedness in higher-order networks, unifies them through a mathematical framework, and demonstrates their prevalence and significance across various social systems.

Contribution

It introduces a unified mathematical framework for nestedness measures and analyzes their implications in social systems.

Findings

Nested structure is common in social systems.

Different measures capture complementary aspects of nestedness.

Absence of nestedness indicates distinct mesoscale organization.

Abstract

In contrast to dyadic interactions, higher-order interactions may contain one another, with subgroups naturally embedded within larger groups. These containment patterns arise empirically in ecology, sociology, computer science and the science of science, and have been studied under the names nestedness, simpliciality, encapsulation, and inclusion. In this chapter, we review each of these measures and unify them through a mathematical object known as the encapsulation directed acyclic graph, formulating each measure as a function of its properties. We demonstrate that nested structure is prevalent in social systems across several domains, show that different measures capture complementary aspects of this structure, and find that the absence of nestedness can itself be a powerful indicator of the mesoscale organization of a system.