Concentration and regularization of random graphs

• Published in: Random structures & algorithms Vol. 51; no. 3; pp. 538 - 561
• Main Authors: Le, Can M., Levina, Elizaveta, Vershynin, Roman
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc 01.10.2017
• Subjects: community detection; concentration; Economic models; graph Laplacian; Graph theory; Graphs; Random graphs; Regularization; sparse networks

This paper studies how close random graphs are typically to their expectations. We interpret this question through the concentration of the adjacency and Laplacian matrices in the spectral norm. We study inhomogeneous Erdös‐Rényi random graphs on n vertices, where edges form independently and possib...