Non-backtracking spectra of weighted inhomogeneous random graphs

DOI10.4171/MSL/34MaRDI QIDQ2694728

Ludovic Stephan, Laurent Massoulié

Publication date: 4 April 2023

Published in: Mathematical Statistics and Learning (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.07408

zbMATH Keywords

random graphscommunity detectionnon-backtracking matrix

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Random matrices (probabilistic aspects) (60B20) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

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Cites Work

• The local semicircle law for a general class of random matrices
• The singular values and vectors of low rank perturbations of large rectangular random matrices
• The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
• Norms and exclusion theorems
• The largest eigenvalue of small rank perturbations of Hermitian random matrices
• The largest eigenvalues of finite rank deformation of large Wigner matrices: Convergence and nonuniversality of the fluctuations
• The eigenvalues of random symmetric matrices
• Nonbacktracking spectrum of random graphs: community detection and nonregular Ramanujan graphs
• Extremal eigenvalues of critical Erdős-Rényi graphs
• Spectral radii of sparse random matrices
• Consistency of spectral clustering in stochastic block models
• Largest eigenvalues of sparse inhomogeneous Erdős-Rényi graphs
• The largest eigenvalue of rank one deformation of large Wigner matrices
• Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
• Spectral redemption in clustering sparse networks
• Community Detection and Stochastic Block Models
• Proof of the Achievability Conjectures for the General Stochastic Block Model
• THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE
• A useful variant of the Davis–Kahan theorem for statisticians
• Spectral techniques applied to sparse random graphs

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