2024/08/08 by Xiaochun Xu, Francesca Parise, Xu, Xinchen +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #FOS: Electrical engineering #Gene Regulatory Network Analysis #Markov Chains and Monte Carlo Methods #Matrix Theory and Algorithms #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2408.04541
openalex publication_date 2024/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a family of random graph models - termed subgraph generated models (SUGMs) - initially developed by Chandrasekhar and Jackson in which higher-order structures are explicitly included in the network formation process. We use matrix concentration inequalities to show convergence of the adjacency matrix of networks realized from such SUGMs to the expected adjacency matrix as a function of the network size. We apply this result to study concentration of centrality measures (such as degree, eigenvector, and Katz centrality) in sampled networks to the corresponding centralities in the expected network, thus proving that node importance can be predicted from knowledge of the random graph model without the need of exact network data.