相关论文: The HyperKron Graph Model for higher-order feature…

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and…

We introduce a random hypergraph model for core-periphery structure. By leveraging our model's sufficient statistics, we develop a novel statistical inference algorithm that is able to scale to large hypergraphs with runtime that is…

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…

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…

Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…

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…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

Despite the fact that many important problems (including clustering) can be described using hypergraphs, theoretical foundations as well as practical algorithms using hypergraphs are not well developed yet. In this paper, we propose a…

Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs…

The analysis of massive graphs is now becoming a very important part of science and industrial research. This has led to the construction of a large variety of graph models, each with their own advantages. The Stochastic Kronecker Graph…

Hypergraphs offer flexible and robust data representations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitively expensive. Much of the current analysis of hypergraphs…

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…

Generative models for graphs are increasingly becoming a popular tool for researchers to generate realistic approximations of graphs. While in the past, focus was on generating graphs which follow general laws, such as the power law for…

Hypergraph neural networks (HGNN) have recently become attractive and received significant attention due to their excellent performance in various domains. However, most existing HGNNs rely on first-order approximations of hypergraph…

In recent years hypergraphs have emerged as a powerful tool to study systems with multi-body interactions which cannot be trivially reduced to pairs. While highly structured methods to generate synthetic data have proved fundamental for the…

We consider the problem of learning graphical models where the support of the concentration matrix can be decomposed as a Kronecker product. We propose a method that uses the Bayesian hierarchical learning modeling approach. Thanks to the…

Hypergraphs are a powerful abstraction for modeling high-order relations, which are ubiquitous in many fields. A hypergraph consists of nodes and hyperedges (i.e., subsets of nodes); and there have been a number of attempts to extend the…

Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…

Network representation learning and node classification in graphs got significant attention due to the invent of different types graph neural networks. Graph convolution network (GCN) is a popular semi-supervised technique which aggregates…

Modeling and generating graphs is fundamental for studying networks in biology, engineering, and social sciences. However, modeling complex distributions over graphs and then efficiently sampling from these distributions is challenging due…