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A variety of metrics have been proposed to measure the relative importance of nodes in a network. One of these, alpha-centrality [Bonacich, 2001], measures the number of attenuated paths that exist between nodes. We introduce a normalized…
We consider the decentralized optimization problem, where a network of $n$ agents aims to collaboratively minimize the average of their individual smooth and convex objective functions through peer-to-peer communication in a directed graph.…
We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity,…
Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to…
Understanding and quantifying node importance is a fundamental problem in network science and engineering, underpinning a wide range of applications such as influence maximization, social recommendation, and network dismantling. Prior…
We study the task of clustering in directed networks. We show that using the eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than all common methods which are based on a combination of data regularization and SVD…
Directed graphs have asymmetric connections, yet the current graph clustering methodologies cannot identify the potentially global structure of these asymmetries. We give a spectral algorithm called di-sim that builds on a dual measure of…
We propose a novel approach for learning node representations in directed graphs, which maintains separate views or embedding spaces for the two distinct node roles induced by the directionality of the edges. We argue that the previous…
From social networks to protein complexes to disease genomes to visual data, hypergraphs are everywhere. However, the scope of research studying deep learning on hypergraphs is still quite sparse and nascent, as there has not yet existed an…
A new measure $c(e)$ of the centrality of an edge $e$ in an undirected graph $G$ is introduced. It is based on the variation of the Kemeny constant of the graph after removing the edge $e$. The new measure is designed in such a way that the…
Graph neural networks (GNNs) face significant challenges with class imbalance, leading to biased inference results. To address this issue in heterogeneous graphs, we propose a novel framework that combines Graph Neural Network (GNN) and…
We consider the problem of inferring the unobserved edges of a graph from data supported on its nodes. In line with existing approaches, we propose a convex program for recovering a graph Laplacian that is approximately diagonalizable by a…
In graph signal processing, learning the weighted connections between nodes from a set of sample signals is a fundamental task when the underlying relationships are not known a priori. This task is typically addressed by finding a graph…
Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…
Graph Neural Networks (GNNs) have received increasing attention for representation learning in various machine learning tasks. However, most existing GNNs applying neighborhood aggregation usually perform poorly on the graph with…
Recently an increasing amount of research is devoted to the question of how the most influential nodes (seeds) can be found effectively in a complex network. There are a number of measures proposed for this purpose, for instance,…
Many complex systems can be represented as networks, and how a network breaks up into subnetworks or communities is of wide interest. However, the development of a method to detect nodes important to communities that is both fast and…
Identifying the most influential nodes in information networks has been the focus of many research studies. This problem has crucial applications in various contexts, such as controlling the propagation of viruses or rumours in real-world…
An oriented hypergraph is an oriented incidence structure that allows for the generalization of graph theoretic concepts to integer matrices through its locally signed graphic substructure. The locally graphic behaviors are formalized in…
The prevalence of graph-based data has spurred the rapid development of graph neural networks (GNNs) and related machine learning algorithms. Yet, despite the many datasets naturally modeled as directed graphs, including citation, website,…