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Graph embedding methods embed the nodes in a graph in low dimensional vector space while preserving graph topology to carry out the downstream tasks such as link prediction, node recommendation and clustering. These tasks depend on a…

Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…

The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…

We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for…

Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…

Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these…

The Random Dot Product Graph (RDPG) is a generative model for relational data, where nodes are represented via latent vectors in low-dimensional Euclidean space. RDPGs crucially postulate that edge formation probabilities are given by the…

Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed…

The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods…

Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis…

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…

Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning…

Network embedding has attracted an increasing attention over the past few years. As an effective approach to solve graph mining problems, network embedding aims to learn a low-dimensional feature vector representation for each node of a…

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…

Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…

The success of graph embeddings or node representation learning in a variety of downstream tasks, such as node classification, link prediction, and recommendation systems, has led to their popularity in recent years. Representation learning…

This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…

A dot-product representation of a graph is a mapping of its vertices to vectors of length $k$ so that vertices are adjacent if and only if the inner product (a.k.a. dot product) of their corresponding vertices exceeds some threshold.…

Vector representations of graphs and relational structures, whether hand-crafted feature vectors or learned representations, enable us to apply standard data analysis and machine learning techniques to the structures. A wide range of…

Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. While achieving competitive performance on a variety of network inference tasks such as node classification and link prediction, these…