Related papers: Computing Cliques and Cavities in Networks
We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…
Maximal clique enumeration is a fundamental graph mining task, but its utility is often limited by computational intractability and highly redundant output. To address these challenges, we introduce \emph{$\rho$-dense aggregators}, a novel…
In this paper, we present a number of network-analysis algorithms in the external-memory model. We focus on methods for large naturally sparse graphs, that is, n-vertex graphs that have O(n) edges and are structured so that this sparsity…
We study maximal cliques in the collinearity graphs of Desarguesian nets, give some structural results and some numerical information. In particular, we show for Desarguesian nets that the set consisting of a point $x$ together with all its…
Cliques, groups of fully connected nodes in a network, are often used to study group dynamics of complex systems. In real-world settings, group dynamics often have a temporal component. For example, conference attendees moving from one…
Finding large cliques or cliques missing a few edges is a fundamental algorithmic task in the study of real-world graphs, with applications in community detection, pattern recognition, and clustering. A number of effective…
Community structure identification has been an important research topic in complex networks and there has been many algorithms proposed so far to detect community structures in complex networks, where most of the algorithms are not suitable…
Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…
De novo DNA assembly is a fundamental task in Bioinformatics, and finding Eulerian paths on de Bruijn graphs is one of the dominant approaches to it. In most of the cases, there may be no one order for the de Bruijn graph that works well…
We present a novel method for detecting communities in bipartite networks. Based on an extension of the $k$-clique community detection algorithm, we demonstrate how modular structure in bipartite networks presents itself as overlapping…
Automatic detection of relevant groups of nodes in large real-world graphs, i.e. community detection, has applications in many fields and has received a lot of attention in the last twenty years. The most popular method designed to find…
Finding dense components in graphs is of great importance in analyzing the structure of networks. Popular and computationally feasible frameworks for discovering dense subgraphs are core and truss decompositions. Recently, Sariyuce et al.…
Finding complete subgraphs in a graph, that is, cliques, is a key problem and has many real-world applications, e.g., finding communities in social networks, clustering gene expression data, modeling ecological niches in food webs, and…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
Clustering and community structure is crucial for many network systems and the related dynamic processes. It has been shown that communities are usually overlapping and hierarchical. However, previous methods investigate these two…
We propose an unsupervised approach for learning vertex orderings for the maximum clique problem by framing it within a permutation-based framework. We transform the combinatorial constraints into geometric relationships such that the…
Brain extraction is a fundamental step for most brain imaging studies. In this paper, we investigate the problem of skull stripping and propose complementary segmentation networks (CompNets) to accurately extract the brain from T1-weighted…
The recursive removal of leaves (dead end vertices) and their neighbors from an undirected network results, when this pruning algorithm stops, in a so-called core of the network. This specific subgraph should be distinguished from…
To understand the structure of a network, it can be useful to break it down into its constituent pieces. This is the approach taken in a multitude of successful network analysis methods, such as motif analysis. These methods require one to…
Subnetwork extraction using community detection methods is commonly used to study the brain's modular structure. Recent studies indicated that certain brain regions are known to interact with multiple subnetworks. However, most existing…