Related papers: Clique Matrices for Statistical Graph Decompositio…
The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of…
We tackle the problem of counting the number of $k$-cliques in large-scale graphs, for any constant $k \ge 3$. Clique counting is essential in a variety of applications, among which social network analysis. Due to its computationally…
We prove that if $G$ is a sparse graph --- it belongs to a fixed class of bounded expansion $\mathcal{C}$ --- and $d\in \mathbb{N}$ is fixed, then the $d$th power of $G$ can be partitioned into cliques so that contracting each of these…
A prominent tool in many problems involving metric spaces is a notion of randomized low-diameter decomposition. Loosely speaking, $\beta$-decomposition refers to a probability distribution over partitions of the metric into sets of low…
Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
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…
Mining dense quasi-cliques is a well-known clustering task with applications ranging from social networks over collaboration graphs to document analysis. Recent work has extended this task to multiple graphs; i.e. the goal is to find groups…
Motivated by applications in social network community analysis, we introduce a new clustering paradigm termed motif clustering. Unlike classical clustering, motif clustering aims to minimize the number of clustering errors associated with…
This paper is about: (1) bounds on the number of cliques in a graph in a particular class, and (2) algorithms for listing all cliques in a graph. We present a simple algorithm that lists all cliques in an $n$-vertex graph in O(n) time per…
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…
This publication serves as an overview of clique topology -- a novel matrix analysis technique used to extract structural features from neural activity data that contains hidden nonlinearities. We highlight work done by Gusti et al. which…
We address the problem of enumerating all maximal clique-partitions of an undirected graph and present an algorithm based on the observation that every maximal clique-partition can be produced from the maximal clique-cover of the graph by…
We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure---the property that pairs of vertices with common neighbors tend to be…
Many problems in machine learning can be expressed by means of a graph with nodes representing training samples and edges representing the relationship between samples in terms of similarity, temporal proximity, or label information. Graphs…
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…
We present an approach to representing large sets of mutual exclusions, also known as mutexes or mutex constraints. These are the types of constraints that specify the exclusion of some properties, events, processes, and so on. They are…
In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between…
How do vertices exert influence in graph data? We develop a framework for edge clustering, a new method for exploratory data analysis that reveals how both vertices and edges collaboratively accomplish directed influence in graphs,…
NodeTrix representations are a popular way to visualize clustered graphs; they represent clusters as adjacency matrices and inter-cluster edges as curves connecting the matrix boundaries. We study the complexity of constructing NodeTrix…