Related papers: Fast Computation of Generalized Eigenvectors for M…

Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…

With the development of quantum algorithms, high-cost computations are being scrutinized in the hope of a quantum advantage. While graphs offer a convenient framework for multiple real-world problems, their analytics still comes with high…

The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…

Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…

Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…

Graph partitioning (GP), a.k.a. community detection, is a classic problem that divides the node set of a graph into densely-connected blocks. Following prior work on the IEEE HPEC Graph Challenge benchmark and recent advances in graph…

Recently a variety of methods have been developed to encode graphs into low-dimensional vectors that can be easily exploited by machine learning algorithms. The majority of these methods start by embedding the graph nodes into a…

We focus in this work on the estimation of the first $k$ eigenvectors of any graph Laplacian using filtering of Gaussian random signals. We prove that we only need $k$ such signals to be able to exactly recover as many of the smallest…

Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…

Let G=(V,E) be an undirected graph, lambda_k be the k-th smallest eigenvalue of the normalized laplacian matrix of G. There is a basic fact in algebraic graph theory that lambda_k > 0 if and only if G has at most k-1 connected components.…

In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and…

Large-scale eigenvalue computations on sparse matrices are a key component of graph analytics techniques based on spectral methods. In such applications, an exhaustive computation of all eigenvalues and eigenvectors is impractical and…

Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…

This paper discusses how to generate general graph node embeddings from knowledge graph representations. The embedded space is composed of a number of sub-features to mimic both local affinity and remote structural relevance. These…

In this paper we propose a lightning fast graph embedding method called one-hot graph encoder embedding. It has a linear computational complexity and the capacity to process billions of edges within minutes on standard PC -- making it an…

Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…

Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and…

Learning efficient graph representation is the key to favorably addressing downstream tasks on graphs, such as node or graph property prediction. Given the non-Euclidean structural property of graphs, preserving the original graph data's…

We review the properties of eigenvectors for the graph Laplacian matrix, aiming at predicting a specific eigenvalue/vector from the geometry of the graph. After considering classical graphs for which the spectrum is known, we focus on…

Spectral embedding of graphs uses the top k non-trivial eigenvectors of the random walk matrix to embed the graph into R^k. The primary use of this embedding has been for practical spectral clustering algorithms [SM00,NJW02]. Recently,…