Related papers: Edge-exchangeable graphs and sparsity (NIPS 2016)
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The…
Analyzing massive complex networks yields promising insights about our everyday lives. Building scalable algorithms to do so is a challenging task that requires a careful analysis and an extensive evaluation. However, engineering such…
The ability of a peer-to-peer (P2P) system to effectively host decentralized applications often relies on the availability of a peer-sampling service, which provides each participant with a random sample of other peers. Despite the…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as a measure of inherent diversity, of different network parameters. It utilizes sparsity index…
A stationary random graph is a random rooted graph whose distribution is invariant under re-rooting along the simple random walk. We adapt the entropy technique developed for Cayley graphs and show in particular that stationary random…
We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration…
This paper introduces a nonparametric framework for the setting where multiple networks are observed on the same set of nodes, also known as multiplex networks. Our objective is to provide a simple parameterization which explicitly captures…
While (message-passing) graph neural networks have clear limitations in approximating permutation-equivariant functions over graphs or general relational data, more expressive, higher-order graph neural networks do not scale to large…
Graph generation is a critical yet challenging task, as empirical analyses require a deep understanding of complex, non-Euclidean structures. Diffusion models have recently made significant advances in graph generation, but these models are…
Given an $n$-vertex graph $G$ with minimum degree at least $d n$ for some fixed $d > 0$, the distribution $G \cup \mathbb{G}(n,p)$ over the supergraphs of $G$ is referred to as a (random) {\sl perturbation} of $G$. We consider the…
Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…
There has been an increased interest in applying machine learning techniques on relational structured-data based on an observed graph. Often, this graph is not fully representative of the true relationship amongst nodes. In these settings,…
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…
A variety of machine learning tasks---e.g., matrix factorization, topic modelling, and feature allocation---can be viewed as learning the parameters of a probability distribution over bipartite graphs. Recently, a new class of models for…
In this paper we consider a dynamic Erd\H{o}s-R\'enyi graph in which edges, according to an alternating renewal process, change from present to absent and vice versa. The objective is to estimate the on- and off-time distributions while…
Graphs are ubiquitous in social networks and biochemistry, where Graph Neural Networks (GNN) are the state-of-the-art models for prediction. Graphs can be evolving and it is vital to formally model and understand how a trained GNN responds…
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…
Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…