Related papers: Subsampling large graphs and invariance in network…

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural…

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…

To accelerate the training of graph convolutional networks (GCNs) on real-world large-scale sparse graphs, downsampling methods are commonly employed as a preprocessing step. However, the effects of graph sparsity and topological structure…

Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how…

We analyse the performance of simple distributed colouring algorithms under the assumption that the input graph is a hyperbolic random graph (HRG), a generative model capturing key properties of real-world networks such as power-law degree…

The problem of learning the structure of a high dimensional graphical model from data has received considerable attention in recent years. In many applications such as sensor networks and proteomics it is often expensive to obtain samples…

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…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

The sampling of graph signals has recently drawn much attention due to the wide applications of graph signal processing. While a lot of efficient methods and interesting results have been reported to the sampling of band-limited or smooth…

We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory…

Graph Convolutional Networks (GCNs) have received significant attention from various research fields due to the excellent performance in learning graph representations. Although GCN performs well compared with other methods, it still faces…

In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…

This paper studies causal inference with observational data from a single large network. We consider a nonparametric model with interference in both potential outcomes and selection into treatment. Specifically, both stages may be the…

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…

Graph randomization techniques play a crucial role in network analysis, allowing researchers to assess the statistical significance of observed network properties and distinguish meaningful patterns from random fluctuations. In this survey…

In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are as diverse as the networks they…

Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex…

Link prediction systems (e.g. recommender systems) typically use graph topology as one of their main sources of information. However, automorphisms and related properties of graphs beget inherent limits in predictability. We calculate hard…

We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…