Relating topological determinants of complex networks to their spectral properties: structural and dynamical effects
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The largest eigenvalue of a network’s adjacency matrix and its associated principal eigenvector are key elements for determining the topological structure and the properties of dynamical processes mediated by it. We present a physically grounded expression relating the value of the largest eigenvalue of a given network to the largest eigenvalue of two network subgraphs, considered as isolated: the hub with its immediate neighbors and the densely connected set of nodes with maximum K -core index. We validate this formula by showing that it predicts, with good accuracy, the largest eigenvalue of a large set of synthetic and real-world topologies. We also present evidence of the consequences of these findings for broad classes of dynamics taking place on the networks. As a by-product, we reveal that the spectral properties of heterogeneous networks built according to the linear preferential attachment model are qualitatively different from those of their static counterparts.
CitationCastellano, C., Pastor-Satorras, R. Relating topological determinants of complex networks to their spectral properties: structural and dynamical effects. "Physical Review X", 27 Octubre 2017, vol. 7, núm. 4, p. 1-12.