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This paper proposes a new algorithm for solving maximal cliques for simple undirected graphs using the theory of prime numbers. A novel approach using prime numbers is used to find cliques and ends with a discussion of the algorithm.

Data Structures and Algorithms · Computer Science 2007-05-23 Dhananjay D. Kulkarni , Shekhar Verma , Prashant

Many methods have been proposed for community detection in networks, but most of them do not take into account additional information on the nodes that is often available in practice. In this paper, we propose a new joint community…

Machine Learning · Statistics 2016-12-13 Yuan Zhang , Elizaveta Levina , Ji Zhu

A canonical problem in graph mining is the detection of dense communities. This problem is exacerbated for a graph with a large order and size -- the number of vertices and edges -- as many community detection algorithms scale poorly. In…

Social and Information Networks · Computer Science 2015-02-17 Heng Wang , Da Zheng , Randal Burns , Carey Priebe

Although the inference of global community structure in networks has recently become a topic of great interest in the physics community, all such algorithms require that the graph be completely known. Here, we define both a measure of local…

Data Analysis, Statistics and Probability · Physics 2008-04-12 Aaron Clauset

The `random intersection graph with communities' models networks with communities, assuming an underlying bipartite structure of groups and individuals. Each group has its own internal structure described by a (small) graph, while groups…

Probability · Mathematics 2019-10-23 Remco van der Hofstad , Júlia Komjáthy , Viktória Vadon

Community detection in multilayer networks, which aims to identify groups of nodes exhibiting similar connectivity patterns across multiple network layers, has attracted considerable attention in recent years. Most existing methods are…

Methodology · Statistics 2026-01-26 Dapeng Shi , Haoran Zhang , Tiandong Wang , Junhui Wang

Complex real-world networks commonly reveal characteristic groups of nodes like communities and modules. These are of value in various applications, especially in the case of large social and information networks. However, while numerous…

Social and Information Networks · Computer Science 2013-12-30 Lovro Šubelj , Marko Bajec

We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…

Statistical Mechanics · Physics 2009-11-10 M. E. J. Newman , M. Girvan

Community structure is of paramount importance for the understanding of complex networks. Consequently, there is a tremendous effort in order to develop efficient community detection algorithms. Unfortunately, the issue of a fair assessment…

Social and Information Networks · Computer Science 2017-11-28 Jebabli Malek , Cherifi Hocine , Cherifi Chantal , Hamouda Atef

Given a set ${\cal AL}$ of community detection algorithms and a graph $G$ as inputs, we propose two ensemble methods $\mathtt{EnDisCO}$ and $\mathtt{MeDOC}$ that (respectively) identify disjoint and overlapping communities in $G$.…

Social and Information Networks · Computer Science 2016-09-19 Tanmoy Chakraborty , Noseong Park , V. S. Subrahmanian

Community detection is an important research topic in complex networks. We present the employment of a genetic algorithm to detect communities in complex networks which is based on optimizing network modularity. It does not need any prior…

Physics and Society · Physics 2007-11-06 Mursel Tasgin , Amac Herdagdelen , Haluk Bingol

Many methods have been proposed to detect communities, not only in plain, but also in attributed, directed or even dynamic complex networks. In its simplest form, a community structure takes the form of a partition of the node set. From the…

Social and Information Networks · Computer Science 2014-10-22 Günce Keziban Orman , Vincent Labatut , Marc Plantevit , Jean-François Boulicaut

Multilayer and multiplex networks are becoming common network data sets in recent times. We consider the problem of identifying the common community structure for a special type of multilayer networks called multi-relational networks. We…

Social and Information Networks · Computer Science 2020-04-08 Sharmodeep Bhattacharyya , Shirshendu Chatterjee

Discovery of communities in complex networks is a topic of considerable recent interest within the complex systems community. Due to the dynamic and rapidly evolving nature of large-scale networks, like online social networks, the notion of…

Social and Information Networks · Computer Science 2018-10-04 Nasheen Nur , Wenwen Dou , Xi Niu , Siddharth Krishnan , Noseong Park

We develop the theory of sparse multiplex networks with partially overlapping links based on their local tree-likeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary…

Visualization of the adjacency matrix enables us to capture macroscopic features of a network when the matrix elements are aligned properly. Community structure, a network consisting of several densely connected components, is a…

Physics and Society · Physics 2023-07-11 Masaki Ochi , Tatsuro Kawamoto

Community detection refers to the task of discovering closely related subgraphs to understand the networks. However, traditional community detection algorithms fail to pinpoint a particular kind of community. This limits its applicability…

Social and Information Networks · Computer Science 2022-10-18 Xixi Wu , Yun Xiong , Yao Zhang , Yizhu Jiao , Caihua Shan , Yiheng Sun , Yangyong Zhu , Philip S. Yu

Overlapped community detection in social networks has become an important research area with the increasing popularity and complexity of the networks. Most of the existing solutions are either centralized or parallel algorithms, which are…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-03-02 Dibakar Saha , Partha Sarathi Mandal

Community detection is a critical challenge in analysing real graphs, including social, transportation, citation, cybersecurity, and many other networks. This article proposes three new, general, hierarchical frameworks to deal with this…

Social and Information Networks · Computer Science 2023-05-25 Łukasz Brzozowski , Grzegorz Siudem , Marek Gagolewski

Overlapping community detection is a key problem in graph mining. Some research has considered applying graph convolutional networks (GCN) to tackle the problem. However, it is still challenging to incorporate deep graph convolutional…

Artificial Intelligence · Computer Science 2024-10-01 Md Nurul Muttakin , Md Iqbal Hossain , Md Saidur Rahman
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