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Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…
Continual learning on graphs tackles the problem of training a graph neural network (GNN) where graph data arrive in a streaming fashion and the model tends to forget knowledge from previous tasks when updating with new data. Traditional…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, $\epsilon$-graphs and $k$-NN graphs can lead to poor performance…
We introduce a graph renormalization procedure based on the coarse-grained Laplacian, which generates reduced-complexity representations for characteristic scales identified through the spectral gap. This method retains both diffusion…
Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…
Graph embeddings are a ubiquitous tool for machine learning tasks, such as node classification and link prediction, on graph-structured data. However, computing the embeddings for large-scale graphs is prohibitively inefficient even if we…
In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and…
The problem of sparsifying a graph or a hypergraph while approximately preserving its cut structure has been extensively studied and has many applications. In a seminal work, Bencz\'ur and Karger (1996) showed that given any $n$-vertex…
The spectrum of a network or graph $G=(V,E)$ with adjacency matrix $A$, consists of the eigenvalues of the normalized Laplacian $L= I - D^{-1/2} A D^{-1/2}$. This set of eigenvalues encapsulates many aspects of the structure of the graph,…
Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…
This paper aims to provide a novel design of a multiscale framelet convolution for spectral graph neural networks (GNNs). While current spectral methods excel in various graph learning tasks, they often lack the flexibility to adapt to…
This work introduces a highly scalable spectral graph densification framework for learning resistor networks with linear measurements, such as node voltages and currents. We prove that given $O(\log N)$ pairs of voltage and current…
We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…
In this paper, we focus on fraud detection on a signed graph with only a small set of labeled training data. We propose a novel framework that combines deep neural networks and spectral graph analysis. In particular, we use the node…
Graph learning plays a central role in many data mining and machine learning tasks, such as manifold learning, data representation and analysis, dimensionality reduction, clustering, and visualization. In this work, we propose a highly…
Graph comparison is a fundamental operation in data mining and information retrieval. Due to the combinatorial nature of graphs, it is hard to balance the expressiveness of the similarity measure and its scalability. Spectral analysis…
We investigate connections between the symmetries (automorphisms) of a graph and its spectral properties. Whenever a graph has a symmetry, i.e. a nontrivial automorphism $\phi$, it is possible to use $\phi$ to decompose any matrix…
A basic fact in spectral graph theory is that the number of connected components in an undirected graph is equal to the multiplicity of the eigenvalue zero in the Laplacian matrix of the graph. In particular, the graph is disconnected if…
Graph Neural Networks (GNNs) have emerged as powerful tools for various graph mining tasks, yet existing scalable solutions often struggle to balance execution efficiency with prediction accuracy. These difficulties stem from iterative…