Structural Sparsity of Complex Networks: Bounded Expansion in Random Models and Real-World Graphs

TL;DR

This paper shows that many real-world networks and certain models have bounded expansion, enabling efficient algorithms, while others like Kleinberg and Barabasi-Albert do not, supported by empirical data.

Contribution

It establishes bounded expansion as a key property of real-world networks and analyzes various models to identify which exhibit this sparsity feature.

Findings

Real-world networks exhibit bounded expansion.

Certain random models like sparse degree sequences have bounded expansion.

Kleinberg and Barabasi-Albert models have unbounded expansion.

Abstract

This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several common network models regarding their structural sparsity. We show that, with high probability, (1) graphs sampled with a prescribed s parse degree sequence; (2) perturbed bounded-degree graphs; (3) stochastic block models with small probabilities; result in graphs of bounded expansion. In contrast, we show that the Kleinberg and the Barabasi-Albert model have unbounded expansion. We support our findings with empirical measurements on a corpus of real-world networks.