澄清度熵和度-度相关性与网络鲁棒性的关系
Clarifying How Degree Entropies and Degree-Degree Correlations Relate to Network Robustness
摘要：
人们经常声称，网络的度分布的熵是其鲁棒性的代理。在这里，我们澄清度分布熵和巨组件的鲁棒性节点删除之间的联系，表明前者只是设置一个下界，后者随机配置的网络时，没有其他网络特性被指定。此外，我们表明，对于遵循相同形式的度分布的固定预期度的网络，度分布熵并不表示鲁棒性。通过对比，证明了剩余度熵与鲁棒性之间存在正单调关系，并给出了对数正态分布下剩余度熵的解析表达式。我们还表明，度-度相关性本身并不表明网络对真实网络的鲁棒性。我们提出了一个调整，如何测量的互信息，更好地封装相关的鲁棒性的结构属性。
英文摘要：
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 degree distribution entropy is not indicative of robustness. By contrast, we show that the remaining degree entropy and robustness have a positive monotonic relationship and give an analytic expression for the remaining degree entropy of the log-normal distribution. We also show that degree-degree correlations are not by themselves indicative of a network's robustness for real networks. We propose an adjustment to how mutual information is measured which better encapsulates structural properties related to robustness.
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