Mixing patterns in graphs with higher-order structure

TL;DR

This paper investigates the percolation properties of higher-order networks with clustering and subgraph-based mixing, introducing a generating function approach and a Monte Carlo algorithm to analyze and generate such networks.

Contribution

It presents a new analytical framework using generating functions and a Monte Carlo algorithm for modeling higher-order networks with clustering and mixing.

Findings

Network microstructure influences global properties.

The model improves over edge-based theory in empirical network representation.

Clustering significantly affects percolation thresholds.

Abstract

In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our analytical method is based on generating functions. We also propose a Monte Carlo graph generation algorithm to draw random networks from the ensemble of graphs with fixed statistics. We use our model to understand the effect that network microstructure has, through the arrangement of clustering, on the global properties. Finally, we use an edge disjoint clique cover to represent empirical networks using our formulation, finding the resultant model offers a significant improvement over edge-based theory.