Related papers: A cluster expansion approach to exponential random…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
Yin, Rinaldo, and Fadnavis classified the extremal behavior of the edge-triangle exponential random graph model by first taking the network size to infinity, then the parameters diverging to infinity along straight lines. Lubetzky and Zhao…
A/B testing is a standard approach for evaluating the effect of online experiments; the goal is to estimate the `average treatment effect' of a new feature or condition by exposing a sample of the overall population to it. A drawback with…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…
We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs…
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…
In this paper, a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
Ensembles of networks arise in various fields where multiple independent networks are observed on the same set of nodes, for example, a collection of brain networks constructed on the same brain regions for different individuals. However,…
We study the evolution of random graphs where edges are added one by one between pairs of weighted vertices so that resulting graphs are scale-free with the degree exponent $\gamma$. We use the branching process approach to obtain scaling…
The global clustering coefficient is an effective measure for analyzing and comparing the structures of complex networks. The random annulus graph is a modified version of the well-known Erd\H{o}s-R\'{e}nyi random graph. It has been…
Under quite general conditions critical phenomena can be described with high order linked cluster expansions. The coefficients of the series admit a graphical expansion that is generated with the aid of computers. Our generalization of…
We introduce two models of inclusion hierarchies: Random Graph Hierarchy (RGH) and Limited Random Graph Hierarchy (LRGH). In both models a set of nodes at a given hierarchy level is connected randomly, as in the Erd\H{o}s-R\'{e}nyi random…
We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the…
We propose a generalization of the linked-cluster expansions to study driven-dissipative quantum lattice models, directly accessing the thermodynamic limit of the system. Our method leads to the evaluation of the desired extensive property…
Edge expansion is a parameter indicating how well-connected a graph is. It is useful for designing robust networks, analysing random walks or information flow through a network and is an important notion in theoretical computer science.…
The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paper we analyze the Glauber dynamics of the…
This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes and degree distributions, identifying four regimes: (i) a dense…