Related papers: Limits of local algorithms over sparse random grap…
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…
Clustering is a commonplace problem in many areas of data science, with applications in biology and bioinformatics, understanding chemical structure, image segmentation, building recommender systems, and many more fields. While there are…
Local sets, a graph structure invariant under local complementation, have been originally introduced in the context of quantum computing for the study of quantum entanglement within the so-called graph state formalism. A local set in a…
Algorithms for node clustering typically focus on finding homophilous structure in graphs. That is, they find sets of similar nodes with many edges within, rather than across, the clusters. However, graphs often also exhibit heterophilous…
The Maximal Independent Set (MIS) problem is one of the basics in the study of locality in distributed graph algorithms. This paper presents an extremely simple randomized algorithm providing a near-optimal local complexity for this…
Given an underlying graph, we consider the following \emph{dynamics}: Initially, each node locally chooses a value in $\{-1,1\}$, uniformly at random and independently of other nodes. Then, in each consecutive round, every node updates its…
Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping…
Local general depth ($LGD$) functions are used for describing the local geometric features and mode(s) in multivariate distributions. In this paper, we undertake a rigorous systematic study of $LGD$ and establish several analytical and…
Local clustering aims to identify a cluster within a given graph that includes a designated seed node or a significant portion of a group of seed nodes. This cluster should be well-characterized, i.e., it has a high number of internal edges…
In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters which are cohesive in that close-by pairs of nodes are assigned to the same cluster with high probability.…
Kim defined a very general combinatorial abstraction of the diameter of polytopes called subset partition graphs to study how certain combinatorial properties of such graphs may be achieved in lower bound constructions. Using Lov\'asz'…
Recently Rubinfeld et al. (ICS 2011, pp. 223--238) proposed a new model of sublinear algorithms called \emph{local computation algorithms}. In this model, a computation problem $F$ may have more than one legal solution and each of them…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
We present a novel hierarchical graph clustering algorithm inspired by modularity-based clustering techniques. The algorithm is agglomerative and based on a simple distance between clusters induced by the probability of sampling node pairs.…
Modern graph clustering applications require the analysis of large graphs and this can be computationally expensive. In this regard, local spectral graph clustering methods aim to identify well-connected clusters around a given "seed set"…
We study large-scale, distributed graph clustering. Given an undirected graph, our objective is to partition the nodes into disjoint sets called clusters. A cluster should contain many internal edges while being sparsely connected to other…
Due to the massive size of modern network data, local algorithms that run in sublinear time for analyzing the cluster structure of the graph are receiving growing interest. Two typical examples are local graph clustering algorithms that…
We consider the problem of testing graph cluster structure: given access to a graph $G=(V, E)$, can we quickly determine whether the graph can be partitioned into a few clusters with good inner conductance, or is far from any such graph?…
We use an entropy based method to study two graph maximization problems. We upper bound the number of matchings of fixed size $\ell$ in a $d$-regular graph on $N$ vertices. For $\frac{2\ell}{N}$ bounded away from 0 and 1, the logarithm of…
In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and…