Clarifying How Degree Entropies and Degree-Degree Correlations Relate to Network Robustness

It is often claimed that the entropy of a network's degree distribution is a proxy for its robustness. Here, we clarify the link between degree distribution entropy and giant component robustness to node removal by showing that the former merely sets a lower bound to the latter for randomly configured networks when no other network characteristics are specified. Furthermore, we show that, for networks of fixed expected degree that follow degree distributions of the same form, the relation between degree distribution entropy and robustness is not a functional one. By contrast, there is evidence that the relation between remaining degree entropy and robustness is, in this case, a functional one. We also show that degree-degree correlations, contrary to what is generally assumed, are not by themselves indicative of a network's robustness. We introduce two new algorithms: one that reconfigures a network such that it is disassortative and has a low robustness, and another that swaps the edges in a network while preserving the network's joint degree distribution. We present computed entropies and robustness (as measured by critical fraction) for many artificial and real-world networks to illustrate our results.Comment: 22 pages, 8 figure