Related papers: Fast maximal clique enumeration in weighted tempor…
A temporal network is a mathematical way of precisely representing a time varying relationship among a group of agents. In this paper, we introduce the notion of $(\Delta, \gamma)$-Cliques of a temporal network, where every pair of vertices…
A \emph{Temporal Network} (also known as \emph{Link Stream} or \emph{Time-Varying Graph}) is often used to model a time-varying relationship among a group of agents. It is typically represented as a collection of triplets of the form…
Many real-world networks evolve over time, that is, new contacts appear and old contacts may disappear. They can be modeled as temporal graphs where interactions between vertices (which represent people in the case of social networks) are…
Given a temporal network $\mathcal{G}(\mathcal{V}, \mathcal{E}, \mathcal{T})$, $(\mathcal{X},[t_a,t_b])$ (where $\mathcal{X} \subseteq \mathcal{V}(\mathcal{G})$ and $[t_a,t_b] \subseteq \mathcal{T}$) is said to be a $(\Delta,…
Exact maximum clique finders have progressed to the point where we can investigate cliques in million-node social and information networks, as well as find strongly connected components in temporal networks. We use one such finder to study…
Link streams offer a good model for representing interactions over time. They consist of links $(b,e,u,v)$, where $u$ and $v$ are vertices interacting during the whole time interval $[b,e]$. In this paper, we deal with the problem of…
Dynamics of interactions play an increasingly important role in the analysis of complex networks. A modeling framework to capture this are temporal graphs which consist of a set of vertices (entities in the network) and a set of…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with…
We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. The method exhibits a roughly linear runtime scaling over real-world networks…
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…
Maximal clique enumeration (MCE) is a fundamental problem in graph theory and is used in many applications, such as social network analysis, bioinformatics, intelligent agent systems, cyber security, etc. Most existing MCE algorithms focus…
Finding cohesive subgraphs in a large graph has many important applications, such as community detection and biological network analysis. Clique is often a too strict cohesive structure since communities or biological modules rarely form as…
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…
Maximal clique enumeration appears in various real-world networks, such as social networks and protein-protein interaction networks for different applications. For general graph inputs, the number of maximal cliques can be up to…
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…
Listing dense subgraphs in large graphs plays a key task in varieties of network analysis applications like community detection. Clique, as the densest model, has been widely investigated. However, in practice, communities rarely form as…
A set of vertices in a graph forms a potential maximal clique if there exists a minimal chordal completion in which it is a maximal clique. Potential maximal cliques were first introduced as a key tool to obtain an efficient, though…
As a fundamental task in graph data management, maximal clique enumeration (MCE) has attracted extensive attention from both academic and industrial communities due to its wide range of applications. However, MCE is very challenging as the…
We consider the maintenance of the set of all maximal cliques in a dynamic graph that is changing through the addition or deletion of edges. We present nearly tight bounds on the magnitude of change in the set of maximal cliques, as well as…
Isolation is a concept from the world of clique enumeration that is mostly used to model communities that do not have much contact to the outside world. Herein, a clique is considered isolated if it has few edges connecting it to the rest…