Related papers: Efficient $k$-Clique Listing: An Edge-Oriented Bra…
In this work, we consider the problem of sampling a $k$-clique in a graph from an almost uniform distribution in sublinear time in the general graph query model. Specifically the algorithm should output each $k$-clique with probability…
Finding all maximal $k$-plexes on networks is a fundamental research problem in graph analysis due to many important applications, such as community detection, biological graph analysis, and so on. A $k$-plex is a subgraph in which every…
Identifying dense bipartite subgraphs is a common graph data mining task. Many applications focus on the enumeration of all maximal bicliques (MBs), though sometimes the stricter variant of maximal induced bicliques (MIBs) is of interest.…
Counting k-cliques in a graph is an important problem in graph analysis with many applications such as community detection and graph partitioning. Counting k-cliques is typically done by traversing search trees starting at each vertex in…
Graph analytics attract much attention from both research and industry communities. Due to the linear time complexity, the $k$-core decomposition is widely used in many real-world applications such as biology, social networks, community…
The concept of $k$-defective clique, a relaxation of clique by allowing up-to $k$ missing edges, has been receiving increasing interests recently. Although the problem of finding the maximum $k$-defective clique is NP-hard, several…
Bonne and Censor-Hillel (ICALP 2019) initiated the study of distributed subgraph finding in dynamic networks of limited bandwidth. For the case where the target subgraph is a clique, they determined the tight bandwidth complexity bounds in…
We give the first almost-linear time algorithm for computing the \emph{maximal $k$-edge-connected subgraphs} of an undirected unweighted graph for any constant $k$. More specifically, given an $n$-vertex $m$-edge graph $G=(V,E)$ and a…
Covering and partitioning the edges of a graph into cliques are classical problems at the intersection of combinatorial optimization and graph theory, having been studied through a range of algorithmic and complexity-theoretic lenses.…
In this paper, we present a collection of novel and scalable algorithms designed to tackle the challenges inherent in the $k$-clique densest subgraph problem (\kcdsp) within network analysis. We propose \psctl, a novel algorithm based on…
Dell, Lapinskas and Meeks [DLM SICOMP 2022] presented a general reduction from approximate counting to decision for a class of fine-grained problems that can be viewed as hyperedge counting or detection problems in an implicit hypergraph,…
Graphlets of order $k$ in a graph $G$ are connected subgraphs induced by $k$ nodes (called $k$-graphlets) or by $k$ edges (called edge $k$-graphlets). They are among the interesting subgraphs in network analysis to get insights on both the…
Given a weighted graph $G(V,E)$ with weight $\mathbf w: E\rightarrow Z^{|E|}_{+}$. A $k-$cycle covering is an edge subset $A$ of $E$ such that $G-A$ has no $k-$cycle. The minimum weight of $k-$cycle covering is the weighted covering number…
We are given a graph $G$ with $n$ vertices, where a random subset of $k$ vertices has been made into a clique, and the remaining edges are chosen independently with probability $\tfrac12$. This random graph model is denoted…
Biclustering, also called co-clustering, block clustering, or two-way clustering, involves the simultaneous clustering of both the rows and columns of a data matrix into distinct groups, such that the rows and columns within a group display…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
K-clique percolation is an overlapping community finding algorithm which extracts particular structures, comprised of overlapping cliques, from complex networks. While it is conceptually straightforward, and can be elegantly expressed using…
A $k$-clique is a dense graph, consisting of $k$ fully-connected nodes, that finds numerous applications, such as community detection and network analysis. In this paper, we study a new problem, that finds a maximum set of disjoint…
Cohesive subgraph mining is a fundamental problem in graph theory with numerous real-world applications, such as social network analysis and protein-protein interaction modeling. Among various cohesive subgraphs, the $\gamma$-quasi-clique…
The edge clique cover (ECC) problem -- where the goal is to find a minimum cardinality set of cliques that cover all the edges of a graph -- is a classic NP-hard problem that has received much attention from both the theoretical and…