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Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
Massive networks have shown that the determination of dense subgraphs, where vertices interact a lot, is necessary in order to visualize groups of common interest, and therefore be able to decompose a big graph into smaller structures. Many…
We introduce the graphlet decomposition of a weighted network, which encodes a notion of social information based on social structure. We develop a scalable inference algorithm, which combines EM with Bron-Kerbosch in a novel fashion, for…
Graph clustering aims to divide the graph into different clusters. The recently emerging deep graph clustering approaches are largely built on graph neural networks (GNN). However, GNN is designed for general graph encoding and there is a…
Among the novel metrics used to study the relative importance of nodes in complex networks, k-core decomposition has found a number of applications in areas as diverse as sociology, proteinomics, graph visualization, and distributed system…
The Connected Vertex Cover problem, where the goal is to compute a minimum set of vertices in a given graph which forms a vertex cover and induces a connected subgraph, is a fundamental combinatorial problem and has received extensive…
Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…
Let $G$ be a strongly connected directed graph. We consider the following three problems, where we wish to compute the smallest strongly connected spanning subgraph of $G$ that maintains respectively: the $2$-edge-connected blocks of $G$…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
We tackle the problem of graph partitioning for image segmentation using correlation clustering (CC), which we treat as an integer linear program (ILP). We reformulate optimization in the ILP so as to admit efficient optimization via…
Kernelization algorithms, usually a preprocessing step before other more traditional algorithms, are very special in the sense that they return (reduced) instances, instead of final results. This characteristic excludes the freedom of…
Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…
The $k$-core decomposition is a widely studied summary statistic that describes a graph's global connectivity structure. In this paper, we move beyond using $k$-core decomposition as a tool to summarize a graph and propose using $k$-core…
Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…
Key graph-based problems play a central role in understanding network topology and uncovering patterns of similarity in homogeneous and temporal data. Such patterns can be revealed by analyzing communities formed by nodes, which in turn can…
We present an algorithm that efficiently computes nearly-optimal solutions to a class of combinatorial reconfiguration problems on weighted, undirected graphs. Inspired by societally relevant applications in networked infrastructure…
We propose a weighted common subgraph (WCS) matching algorithm to find the most similar subgraphs in two labeled weighted graphs. WCS matching, as a natural generalization of the equal-sized graph matching or subgraph matching, finds wide…
The CONNECTED VERTEX COVER problem asks for a vertex cover in a graph that induces a connected subgraph. The problem is known to be fixed-parameter tractable (FPT), and is unlikely to have a polynomial sized kernel (under complexity…
Analyzing interconnection structures among underlying entities or objects in a dataset through the use of graph analytics has been shown to provide tremendous value in many application domains. However, graphs are not the primary…
In this paper we propose a new problem of finding the maximal bi-connected partitioning of a graph with a size constraint (MBCPG-SC). With the goal of finding approximate solutions for the MBCPG-SC, a heuristic method is developed based on…