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We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the…

Social and Information Networks · Computer Science 2024-02-27 Zachary Lubberts , Avanti Athreya , Youngser Park , Carey E. Priebe

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…

Statistics Theory · Mathematics 2021-04-21 Anatol E. Wegner , Sofia Olhede

A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…

Probability · Mathematics 2007-05-23 K. B. Athreya , A. P. Ghosh , S. Sethuraman

We study a one parameter family of random graph models that spans a continuum between traditional random graphs of the Erd\H{o}s-R\'enyi type, where there is no underlying structure, and percolation models, where the possible edges are…

Probability · Mathematics 2008-04-02 Oskar Sandberg

We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…

Combinatorics · Mathematics 2013-11-13 Svante Janson , Simone Severini

We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming edges are randomly assigned between its offspring and a…

Probability · Mathematics 2022-01-05 Agelos Georgakopoulos , John Haslegrave

We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…

Statistical Mechanics · Physics 2017-09-13 Reimer Kuehn , Tim Rogers

Random hypergraphs extend the classical notion of random graphs by allowing hyperedges to join more than two vertices, making them well-suited for modeling higher-order interactions in complex systems. Despite their broad applicability,…

Probability · Mathematics 2026-04-08 Yanna J. Kraakman , Clara Stegehuis

We present an algorithm for generating random networks with arbitrary degree distribution and Clustering (frequency of triadic closure). We use this algorithm to generate networks with exponential, power law, and poisson degree…

Statistical Mechanics · Physics 2009-11-10 Erik Volz

Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…

Statistical Mechanics · Physics 2009-10-31 M. E. J. Newman , S. H. Strogatz , D. J. Watts

Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…

Probability · Mathematics 2026-01-14 Remco van der Hofstad , Julia Komjathy , Viktoria Vadon

An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We…

Statistics Theory · Mathematics 2026-03-06 Jonathan R. Stewart , Michael Schweinberger

Random graph models are a recurring tool-of-the-trade for studying network structural properties and benchmarking community detection and other network algorithms. Moreover, they serve as test-bed generators for studying diffusion and…

Physics and Society · Physics 2021-02-16 Dario Fasino , Arianna Tonetto , Francesco Tudisco

The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…

Mathematical Physics · Physics 2015-06-11 Mei Yin

Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…

Physics and Society · Physics 2022-12-28 Judith Brugman , Johan S. H. van Leeuwaarden , Clara Stegehuis

We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the…

Machine Learning · Statistics 2018-11-19 Arun Venkitaraman , Dave Zachariah

We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards…

Combinatorics · Mathematics 2007-05-23 Nikolaos Fountoulakis

Suppose we want to construct some structure on a bounded-degree graph, e.g., an almost maximum matching, and we want to decide about each edge depending only on its constant-radius neighborhood. We examine and compare the strengths of…

Combinatorics · Mathematics 2023-11-03 Endre Csóka

Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…

Social and Information Networks · Computer Science 2019-04-05 E. B. Yudin

Why do many modern neural-network-based graph generative models fail to reproduce typical real-world network characteristics, such as high triangle density? In this work we study the limitations of edge independent random graph models, in…

Machine Learning · Computer Science 2021-11-02 Sudhanshu Chanpuriya , Cameron Musco , Konstantinos Sotiropoulos , Charalampos E. Tsourakakis