  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.
