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Spectral hypergraph sparsification, an attempt to extend well-known spectral graph sparsification to hypergraphs, has been extensively studied over the past few years. For undirected hypergraphs, Kapralov, Krauthgamer, Tardos, and…
One of the biggest huddles faced by researchers studying algorithms for massive graphs is the lack of large input graphs that are essential for the development and test of the graph algorithms. This paper proposes two efficient and highly…
Graph-based techniques and spectral graph theory have enriched the field of machine learning with a variety of critical advances. A central object in the analysis is the graph Laplacian L, which encodes the structure of the graph. We…
Graph Neural Networks (GNNs) have demonstrated remarkable performance in a wide range of tasks, such as node classification, link prediction, and graph classification, by exploiting the structural information in graph-structured data.…
A node separator of a graph is a subset S of the nodes such that removing S and its incident edges divides the graph into two disconnected components of about equal size. In this work, we introduce novel algorithms to find small node…
Graph Transformers (GTs) have made remarkable achievements in graph-level tasks. However, most existing works regard graph structures as a form of guidance or bias for enhancing node representations, which focuses on node-central…
From social science to biology, numerous applications often rely on graphlets for intuitive and meaningful characterization of networks at both the global macro-level as well as the local micro-level. While graphlets have witnessed a…
Graph coarsening is a graph dimensionality reduction technique that aims to construct a smaller and more tractable graph while preserving the essential structural and semantic properties of the original graph. However, most existing methods…
Graph neural networks (GNNs) have demonstrated excellent performance in semi-supervised node classification tasks. Despite this, two primary challenges persist: heterogeneity and heterophily. Each of these two challenges can significantly…
A popular graph clustering method is to consider the embedding of an input graph into R^k induced by the first k eigenvectors of its Laplacian, and to partition the graph via geometric manipulations on the resulting metric space. Despite…
UMAP is a popular neighborhood-preserving dimension reduction (DR) algorithm. However, its application for graph drawing has not been evaluated. Moreover, a naive application of UMAP to graph drawing would include O(nm) time all-pair…
Computing maximum weight independent sets in graphs is an important NP-hard optimization problem. The problem is particularly difficult to solve in large graphs for which data reduction techniques do not work well. To be more precise,…
State-of-the-art Graph Neural Networks (GNNs) have limited scalability with respect to the graph and model sizes. On large graphs, increasing the model depth often means exponential expansion of the scope (i.e., receptive field). Beyond…
Normalized-cut graph partitioning aims to divide the set of nodes in a graph into $k$ disjoint clusters to minimize the fraction of the total edges between any cluster and all other clusters. In this paper, we consider a fair variant of the…
New algorithms for embedding graphs have reduced the asymptotic complexity of finding low-dimensional representations. One-Hot Graph Encoder Embedding (GEE) uses a single, linear pass over edges and produces an embedding that converges…
We propose two spectral algorithms for partitioning nodes in directed graphs respectively with a cyclic and an acyclic pattern of connection between groups of nodes. Our methods are based on the computation of extremal eigenvalues of the…
Graph Neural Network (GNN) on streaming graphs has gained increasing popularity. However, its practical deployment remains challenging, as the inference process relies on Runtime Embedding Computation (RTEC) to capture recent graph changes.…
Feature extraction is an essential task in graph analytics. These feature vectors, called graph descriptors, are used in downstream vector-space-based graph analysis models. This idea has proved fruitful in the past, with spectral-based…
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…
We study the design of local algorithms for massive graphs. A local algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph. We present a local clustering algorithm. Our algorithm finds a…