Related papers: Models of random graph hierarchies
The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…
Social networks as a representation of relational data, often possess multiple types of dependency structures at the same time. There could be clustering (beyond homophily) at a macro level as well as transitivity (a friend's friend is more…
We propose a hierarchical graph neural network (GNN) model that learns how to cluster a set of images into an unknown number of identities using a training set of images annotated with labels belonging to a disjoint set of identities. Our…
The presence of unobserved node specific heterogeneity in Exponential Random Graph Models (ERGM) is a general concern, both with respect to model validity as well as estimation instability. We therefore extend the ERGM by including node…
In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…
We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<\gamma<3$. Degree heterogeneity increases the presence of triangles in…
In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…
Understanding the subgraph distribution in random networks is important for modelling complex systems. In classic Erdos networks, which exhibit a Poissonian degree distribution, the number of appearances of a subgraph G with n nodes and g…
Motivated by the analysis of social networks, we study a model of random networks that has both a given degree distribution and a tunable clustering coefficient. We consider two types of growth processes on these graphs: diffusion and…
Large graphs are present in a variety of domains, including social networks, civil infrastructure, and the physical sciences to name a few. Graph generation is similarly widespread, with applications in drug discovery, network analysis and…
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…
A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under…
Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we…
Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…
A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations, by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that…
In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results…
Graphs with heterophily, where adjacent nodes carry different labels, are prevalent in real-world applications, from social networks to molecular interactions. However, existing spectral Graph Neural Network (GNN) approaches tailored for…
Given an undirected $n$-vertex graph $G(V,E)$ and an integer $k$, let $T_k(G)$ denote the random vertex induced subgraph of $G$ generated by ordering $V$ according to a random permutation $\pi$ and including in $T_k(G)$ those vertices with…
Exponential-family Random Graph Models (ERGMs) constitute a large statistical framework for modeling sparse and dense random graphs, short- and long-tailed degree distributions, covariates, and a wide range of complex dependencies. Special…
The global clustering coefficient serves as a powerful metric for the structural analysis and comparison of complex networks. Random geometric graphs offer a realistic framework for representing the spatial constraints and geometry often…