网络谱的简并性分析
Analysing degeneracies in networks spectra
摘要：
许多真实世界的网络在很少的特征值处表现出高度的退化。我们表明，一个简单的变换网络的邻接矩阵提供了一个理解的起源发生高的多重性的网络光谱。我们发现与简并本征值相关的本征向量揭示了导致简并的结构。由于这些退化很少在模型图中观察到，我们提出了各种癌症网络的结果。这种方法提供了一个机会，以寻找结构的简并可能有一个重要的作用，在网络中。
英文摘要：
Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network's adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks spectra. We find that the eigenvectors associated with the degenerate eigenvalues shed light on the structures contributing to the degeneracy. Since these degeneracies are rarely observed in model graphs, we present results for various cancer networks. This approach gives an opportunity to search for structures contributing to degeneracy which might have an important role in a network.
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