Related papers: Generalised hypergeometric ensembles of random gra…
Statistical ensembles of networks, i.e., probability spaces of all networks that are consistent with given aggregate statistics, have become instrumental in the analysis of complex networks. Their numerical and analytical study provides the…
We propose new generalized multivariate hypergeometric distributions, which extremely resemble the classical multivariate hypergeometric distributions. The proposed distributions are derived based on an urn model approach. In contrast to…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
Inside the discipline of graph theory exists an extension known as the hypergraph. This generalization of graphs includes vertices along with hyperedges consisting of collections of two or more vertices. One well-studied application of this…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
The configuration model is the most natural model to generate a random multigraph with a given degree sequence. We use the notion of dense graph limits to characterize the special form of limit objects of convergent sequences of…
Graphs are used to represent and analyze data in domains as diverse as physics, biology, chemistry, planetary science, and the social sciences. Across domains, random graph models relate generative processes to expected graph properties,…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…
A probabilistic model for random hypergraphs is introduced to represent unary, binary and higher order interactions among objects in real-world problems. This model is an extension of the Latent Class Analysis model, which captures…
We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the…
We give precise estimates on the number of active/inactive half-edges in the configuration model used to generate random regular graphs. This is obtained by analyzing a more general urn model with negative eigenvalues.
Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…
We introduce a model for the randomization of complex networks with geometric structure. The geometric randomization (GR) model assumes a homogeneous distribution of the nodes in an underlying similarity space and uses rewirings of the…
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…
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…
We investigate structural properties of large, sparse random graphs through the lens of "sampling convergence" (Borgs et. al. (2017)). Sampling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a…
We define a general class of network formation models, Statistical Exponential Random Graph Models (SERGMs), that nest standard exponential random graph models (ERGMs) as a special case. We provide the first general results on when these…
This paper presents HGEN that pioneers ensemble learning for heterogeneous graphs. We argue that the heterogeneity in node types, nodal features, and local neighborhood topology poses significant challenges for ensemble learning,…
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…
This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…