2025/05/20 by Sevvandi Kandanaarachchi, Kandanaarachchi, Sevvandi, Cheng Soon Ong +1
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Graph Theory and Algorithms #Limits and Structures in Graph Theory #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.2505.13864
openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Social networks have a small number of large hubs, and a large number of small dense communities. We propose a generative model that captures both hub and dense structures. Based on recent results about graphons on line graphs, our model is a graphon mixture, enabling us to generate sequences of graphs where each graph is a combination of sparse and dense graphs. We propose a new condition on sparse graphs (the max-degree), which enables us to identify hubs. We show theoretically that we can estimate the normalized degree of the hubs, as well as estimate the graphon corresponding to sparse components of graph mixtures. We illustrate our approach on synthetic data, citation graphs, and social networks, showing the benefits of explicitly modeling sparse graphs.