Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects

Claudio Castellano; Romualdo Pastor-Satorras

doi:10.1103/physrevx.7.041024

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arXiv · 1703.10438

Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects

Claudio Castellano·Romualdo Pastor-Satorras

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Abstract

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 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 byproduct, 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.

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physics.soc-ph cond-mat.dis-nn cs.SI

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Claudio Castellano, Romualdo Pastor-Satorras. 2017-03-30. Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects. https://doi.org/10.1103/physrevx.7.041024

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