Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects
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 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.
- Publication:
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Physical Review X
- Pub Date:
- October 2017
- DOI:
- 10.1103/PhysRevX.7.041024
- arXiv:
- arXiv:1703.10438
- Bibcode:
- 2017PhRvX...7d1024C
- Keywords:
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- Physics - Physics and Society;
- Condensed Matter - Disordered Systems and Neural Networks;
- Computer Science - Social and Information Networks
- E-Print:
- 18 pages, 13 figures