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Structural patterns in complex networks through spectral analysis

Estrada, Ernesto (2010) Structural patterns in complex networks through spectral analysis. In: Structural, Syntactic, and Statistical Pattern Recognition. Lecture Notes in Computer Science, 6218 . Springer, pp. 43-59. ISBN 978-3-642-14979-5

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The study of some structural properties of networks is introduced from a graph spectral perspective. First, subgraph centrality of nodes is defined and used to classify essential proteins in a proteomic map. This index is then used to produce a method that allows the identification of superhomogeneous networks. At the same time this method classify non-homogeneous network into three universal classes of structure. We give examples of these classes from networks in different real-world scenarios. Finally, a communicability function is studied and showed as an alternative for defining communities in complex networks. Using this approach a community is unambiguously defined and an algorithm for its identification is proposed and exemplified in a real-world network.