Tree walks and the spectrum of random graphs
Abstract
It is a classic result in spectral graph theory that the empirical spectral measure of random graphs G ( n , p ) converges to the semicircle law in case n p tends to infinity with n . The spectral measure for random graphs G ( n , c / n ) however is less understood. In this work, we combine and extend two combinatorial approaches due to Bauer and Golinelli (2001) and Enriquez and Ménard (2016) and approximate the expected moments of the spectral measure by counting closed walks that span trees.
Fields of Study & Subjects
Topological and Geometric Data Analysis
Complex Network Analysis Techniques
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- European Journal of Combinatorics
- Publisher
- Elsevier BV
- Volume
- 136
- Pages
- 104386–104386
- Publication date
- 17 April 2026
- Language
- EN