Related papers: Listing All Maximal $k$-Plexes in Temporal Graphs
Community search, retrieving the cohesive subgraph which contains the query vertex, has been widely touched over the past decades. The existing studies on community search mainly focus on static networks. However, real-world networks…
Community detection is a discovery tool used by network scientists to analyze the structure of real-world networks. It seeks to identify natural divisions that may exist in the input networks that partition the vertices into coherent…
Community detection is a popular approach to understand the organization of interactions in static networks. For that purpose, the Clique Percolation Method (CPM), which involves the percolation of k-cliques, is a well-studied technique…
Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…
Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the…
Clique counting is a fundamental task in network analysis, and even the simplest setting of $3$-cliques (triangles) has been the center of much recent research. Getting the count of $k$-cliques for larger $k$ is algorithmically challenging,…
Temporal graphs are ubiquitous. Mining communities that are bursting in a period of time is essential to seek emergency events in temporal graphs. Unfortunately, most previous studies for community mining in temporal networks ignore the…
Complex networks often exhibit community structure, with communities corresponding to denser subgraphs in which nodes are closely linked. When modelling systems where interactions extend beyond node pairs to arbitrary numbers of nodes,…
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…
Community detection in graphs has many important and fundamental applications including in distributed systems, compression, image segmentation, divide-and-conquer graph algorithms such as nested dissection, document and word clustering,…
Dynamic networks are a general language for describing time-evolving complex systems, and discrete time network models provide an emerging statistical technique for various applications. It is a fundamental research question to detect the…
Link streams model interactions over time, and a clique in a link stream is defined as a set of nodes and a time interval such that all pairs of nodes in this set interact permanently during this time interval. This notion was introduced…
The degeneracy of an $n$-vertex graph $G$ is the smallest number $d$ such that every subgraph of $G$ contains a vertex of degree at most $d$. We show that there exists a nearly-optimal fixed-parameter tractable algorithm for enumerating all…
$k$-clique listing is a vital graph mining operator with diverse applications in various networks. The state-of-the-art algorithms all adopt a branch-and-bound (BB) framework with a vertex-oriented branching strategy (called VBBkC), which…
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…
Identifying communities from temporal networks facilitates the understanding of potential dynamic relationships among entities, which has already received extensive applications. However, existing methods primarily rely on lower-order…
Finding a Maximum Clique is a classic property test from graph theory; find any one of the largest complete subgraphs in an Erd\"os-R\'enyi G(N, p) random graph. We use Maximum Clique to explore the structure of the problem as a function of…
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…
A clique in a graph is a set of vertices, each of which is adjacent to every other vertex in this set. A k-clique relaxes this requirement, requiring vertices to be within a distance k of each other, rather than directly adjacent. In…
Given a graph, a $k$-plex is a set of vertices in which each vertex is not adjacent to at most $k-1$ other vertices in the set. The maximum $k$-plex problem, which asks for the largest $k$-plex from the given graph, is an important but…