2017/03/31 by Claudio Castellano, Romualdo Pastor-Satorras · 1 citation
Physics and Astronomy · Computer Science · #physics.soc-ph #cond-mat.dis-nn #cs.SI
paper · pdf · doi:10.1103/physrevx.7.041024
published as Phys. Rev. X 7, 041024 (2017) · 18 pages, 13 figures
arxiv created 2017/10/30 · arxiv updated 2017/10/31
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.