2017/05/30 by David Burstein, Burstein, David
Computer Science · Mathematics · Physics and Astronomy · #05C20 #05C50 #05C80 #Combinatorics (math.CO) #Complex Network Analysis Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Opinion Dynamics and Social Influence #Random Matrices and Applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1705.10893
openalex publication_date 2017/05/30 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
The spectral radius of the adjacency matrix can impact both algorithmic\nefficiency as well as the stability of solutions to an underlying dynamical\nprocess. Although much research has considered the distribution of the spectral\nradius for undirected random graph models, as symmetric adjacency matrices are\namenable to spectral analysis, very little work has focused on directed graphs.\nConsequently, we provide novel concentration results for the spectral radius of\nthe directed Chung-Lu random graph model. We emphasize that our concentration\nresults are applicable both asymptotically and to networks of finite size.\nSubsequently, we extend our concentration results to a generalization of the\ndirected Chung-Lu model that allows for community structure.\n