Related papers: Robust Algorithms for Finding Cliques in Random In…
In this article, we develop a clique-based method for social network clustering. We introduce a new index to evaluate the quality of clustering results, and propose an efficient algorithm based on recursive bipartition to maximize an…
A $k$-defective clique is a relaxation of the traditional clique definition, allowing up to $k$ missing edges. This relaxation is crucial in various real-world applications such as link prediction, community detection, and social network…
Message Passing Neural Networks (MPNNs) are a staple of graph machine learning. MPNNs iteratively update each node's representation in an input graph by aggregating messages from the node's neighbors, which necessitates a memory complexity…
Clique and near-clique counts are important graph properties with applications in graph generation, graph modeling, graph analytics, community detection among others. They are the archetypal examples of dense subgraphs. While there are…
The problem of finding the largest induced balanced bipartite subgraph in a given graph is NP-hard. This problem is closely related to the problem of finding the smallest Odd Cycle Transversal. In this work, we consider the following model…
In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an…
An algorithm is developed for finding a close to optimal junction tree of a given graph G. The algorithm has a worst case complexity O(c^k n^a) where a and c are constants, n is the number of vertices, and k is the size of the largest…
We consider the problem of community detection in the Stochastic Block Model with a finite number $K$ of communities of sizes linearly growing with the network size $n$. This model consists in a random graph such that each pair of vertices…
The present work is concerned with community detection. Specifically, we consider a random graph drawn according to the stochastic block model~: its vertex set is partitioned into blocks, or communities, and edges are placed randomly and…
We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…
A "community" in a social network is usually understood to be a group of nodes more densely connected with each other than with the rest of the network. This is an important concept in most domains where networks arise: social,…
We consider the problem of learning latent community structure from multiple correlated networks. We study edge-correlated stochastic block models with two balanced communities, focusing on the regime where the average degree is logarithmic…
We show that the algorithm presented in [J. Fox, T. Roughgarden, C. Seshadhri, F. Wei, and N. Wein. Finding cliques in social networks: A new distribution-free model. SIAM journal on computing, 49(2):448-464, 2020.] can be modified to have…
As a model problem for clustering, we consider the densest k-disjoint-clique problem of partitioning a weighted complete graph into k disjoint subgraphs such that the sum of the densities of these subgraphs is maximized. We establish that…
Community-based graph clustering is one of the most popular topics in the analysis of complex social networks. This type of clustering involves grouping vertices that are considered to share more connections, whereas vertices in different…
Detecting locally, non-overlapping, near-clique densest subgraphs is a crucial problem for community search in social networks. As a vertex may be involved in multiple overlapped local cliques, detecting locally densest sub-structures…
In this paper, we study cliques and chromatic number of inhomogenous random graphs where the individual edge probabilities could be arbitrarily low. We use a recursive method to obtain estimates on the maximum clique size under a mild…
Community detection is a classical problem in the field of graph mining. While most algorithms work on the entire graph, it is often interesting in practice to recover only the community containing some given set of seed nodes. In this…
We present near-optimal algorithms for detecting small vertex cuts in the CONGEST model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete,…
Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such as social…