Related papers: Motif Cut Sparsifiers
A cut $\varepsilon$-sparsifier of a weighted graph $G$ is a re-weighted subgraph of $G$ of (quasi)linear size that preserves the size of all cuts up to a multiplicative factor of $\varepsilon$. Since their introduction by Bencz\'ur and…
Let $G$ be a graph and $S, T \subseteq V(G)$ be (possibly overlapping) sets of terminals, $|S|=|T|=k$. We are interested in computing a vertex sparsifier for terminal cuts in $G$, i.e., a graph $H$ on a smallest possible number of vertices,…
In this paper, we consider the problem of clustering graph nodes and sparsifying graph edges over distributed graphs, when graph edges with possibly edge duplicates are observed at physically remote sites. Although edge duplicates across…
Motif counting plays a crucial role in understanding the structural properties of networks. By computing motif frequencies, researchers can draw key insights into the structural properties of the underlying network. As networks become…
Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, joint interactions of proteins, to name a few. In this work, we propose tools for answering the…
Graph sparsification serves as a foundation for many algorithms, such as approximation algorithms for graph cuts and Laplacian system solvers. As its natural generalization, hypergraph sparsification has recently gained increasing…
We develop a framework for graph sparsification and sketching, based on a new tool, short cycle decomposition -- a decomposition of an unweighted graph into an edge-disjoint collection of short cycles, plus few extra edges. A simple…
Pioneered by Benczur and Karger for cuts in graphs [STOC'96], sparsification is a fundamental topic with wide-ranging applications that has been studied, e.g., for graphs and hypergraphs, in a combinatorial and a spectral setting, and with…
Network community detection is a hot research topic in network analysis. Although many methods have been proposed for community detection, most of them only take into consideration the lower-order structure of the network at the level of…
Graph sparsification aims to reduce the number of edges of a network while maintaining its accuracy for given tasks. In this study, we propose a novel method called GSGAN, which is able to sparsify networks for community detection tasks.…
Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges…
Finding sparse cuts is an important tool in analyzing large-scale distributed networks such as the Internet and Peer-to-Peer networks, as well as large-scale graphs such as the web graph, online social communities, and VLSI circuits. In…
We consider a variation of the spectral sparsification problem where we are required to keep a subgraph of the original graph. Formally, given a union of two weighted graphs $G$ and $W$ and an integer $k$, we are asked to find a $k$-edge…
Frequent and structurally related subgraphs, also known as network motifs, are valuable features of many graph datasets. However, the high computational complexity of identifying motif sets in arbitrary datasets (motif mining) has limited…
Finding dense subnetworks, with density based on edges or more complex structures, such as subgraphs or $k$-cliques, is a fundamental algorithmic problem with many applications. While the problem has been studied extensively in static…
Graph Sparsification aims at compressing large graphs into smaller ones while preserving important characteristics of the input graph. In this work we study Vertex Sparsifiers, i.e., sparsifiers whose goal is to reduce the number of…
Sparsification aims at extracting a reduced core of associations that best preserves both the dynamics and topology of networks while reducing the computational cost of simulations. We show that the semi-metric topology of complex networks…
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…
The identification of motifs--subgraphs that appear significantly more often in a particular network than in an ensemble of randomized networks--has become a ubiquitous method for uncovering potentially important subunits within networks…
Network motifs are recurrent, small-scale patterns of interactions observed frequently in a system. They shed light on the interplay between the topology and the dynamics of complex networks across various domains. In this work, we focus on…