Related papers: Exchangeable Random Networks
We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random…
Estimating the probabilities of linkages in a network has gained increasing interest in recent years. One popular model for network analysis is the exchangeable graph model (ExGM) characterized by a two-dimensional function known as a…
Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, protein-protein interactions, and neuronal…
We propose a model for evolving networks by merging building blocks represented as complete graphs, reminiscent of modules in biological system or communities in sociology. The model shows power-law degree distributions, power-law…
We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…
For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a…
In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…
We present a method for the construction of ensembles of random networks that consist of a single connected component with a given degree distribution. This approach extends the construction toolbox of random networks beyond the…
We introduce a dynamical network model which unifies a number of network families which are individually known to exhibit $q$-exponential degree distributions. The present model dynamics incorporates static (non-growing) self-organizing…
Graph neural networks (GNN) have shown outstanding applications in many fields where data is fundamentally represented as graphs (e.g., chemistry, biology, recommendation systems). In this vein, communication networks comprise many…
Representing networks in a low dimensional latent space is a crucial task with many interesting applications in graph learning problems, such as link prediction and node classification. A widely applied network representation learning…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
The study of probabilistic models for the analysis of complex networks represents a flourishing research field. Among the former, Exponential Random Graphs (ERGs) have gained increasing attention over the years. So far, only linear ERGs…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
Network models are used to study interconnected systems across many physical, biological, and social disciplines. Such models often assume a particular network-generating mechanism, which when fit to data produces estimates of…
A new modelling approach for the analysis of weighted networks with ordinal/polytomous dyadic values is introduced. Specifically, it is proposed to model the weighted network connectivity structure using a hierarchical multilayer…