复杂网络鲁棒性的谱测度
Spectral Measure of Robustness in Complex Networks
摘要：
我们引入自然连通性的概念作为复杂网络的鲁棒性度量。自然连通性具有明确的物理意义和简单的数学公式。它通过量化所有长度的封闭行走的加权数来表征替代路径的冗余。我们表明，自然的连通性，可以从数学上的图谱作为一个平均特征值，它严格单调增加的边缘。我们测试的自然连通性，并将其与其他鲁棒性措施的边缘消除的情况下。我们证明，自然的连接有一个尖锐的歧视，同意我们的直觉。
英文摘要：
We introduce the concept of natural connectivity as a robustness measure of complex networks. The natural connectivity has a clear physical meaning and a simple mathematical formulation. It characterizes the redundancy of alternative paths by quantifying the weighted number of closed walks of all lengths. We show that the natural connectivity can be derived mathematically from the graph spectrum as an average eigenvalue and that it increases strictly monotonically with the addition of edges. We test the natural connectivity and compare it with other robustness measures within a scenario of edge elimination. We demonstrate that the natural connectivity has an acute discrimination which agrees with our intuition.
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