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

arXiv: https://arxiv.org/abs/1703.10438 · HTML: https://mlsanity.com/paper/1703.10438/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2017.

## Built on by (most cited first, 1 of 1)

- [AI sustains higher strategic tension than humans in chess](https://mlsanity.com/paper/2508.13213/) (2025)

## Abstract (arXiv)

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.