Onion structure and network robustness

TL;DR

This paper explores the onion structure in networks, linking it to robustness and expander properties, and introduces a generative algorithm for creating resilient scale-free networks with this structure.

Contribution

It establishes a connection between onion structure and expander properties, and proposes a new algorithm to generate robust networks with this structure.

Findings

Networks with onion structure have high robustness.

Generated networks show resilience against attacks.

Onion-structured networks have large spectral gaps.

Abstract

In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], Schneider et al. proposed a new measure for network robustness and investigated optimal networks with respect to this quantity. For networks with a power-law degree distribution, the optimized networks have an onion structure-high-degree vertices forming a core with radially decreasing degrees and an over-representation of edges within the same radial layer. In this paper we relate the onion structure to graphs with good expander properties (another characterization of robust network) and argue that networks of skewed degree distributions with large spectral gaps (and thus good expander properties) are typically onion structured. Furthermore, we propose a generative algorithm producing synthetic scale-free networks with onion structure, circumventing the optimization procedure of Schneider et al. We validate the robustness of our generated networks against malicious attacks and random removals.