Spectral density of random graphs: convergence properties and application in model fitting
arXiv:2102.11224 · doi:10.1093/comnet/cnab041
Abstract
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific techniques. An important line of research is to develop generic methods able to fit and select the best model among a collection. Approaches based on spectral density (i.e., distribution of the graph adjacency matrix eigenvalues) are appealing for that purpose: they apply to different random graph models. Also, they can benefit from the theoretical background of random matrix theory. This work investigates the convergence properties of model fitting procedures based on the graph spectral density and the corresponding cumulative distribution function. We also review results on the convergence of the spectral density for the most widely used random graph models. Moreover, we explore through simulations the limits of these graph spectral density convergence results, particularly in the case of the block model, where only partial results have been established.
References in corpus (14)
- Emergence of scaling in random networks
- Lethality and centrality in protein networks
- The large-scale organization of metabolic networks
- Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
- Estimating and understanding exponential random graph models
- Spectral distributions of adjacency and Laplacian matrices of random graphs
- Sparse regular random graphs: Spectral density and eigenvectors
- Local semicircle law for random regular graphs
- Spectra of random networks with arbitrary degrees
- Kullback-Leibler Approximation for Probability Measures on Infinite Dimensional Spaces
- On Convergence Properties of Shannon Entropy
- Spectral classes of regular, random, and empirical graphs
- A Graphon Approach to Limiting Spectral Distributions of Wigner-type Matrices
- Higher-Order Spectral Clustering for Geometric Graphs