Related papers: Modularity functions maximization with nonnegative…
Revealing a community structure in a network or dataset is a central problem arising in many scientific areas. The modularity function $Q$ is an established measure quantifying the quality of a community, being identified as a set of nodes…
An efficient and relatively fast algorithm for the detection of communities in complex networks is introduced. The method exploits spectral properties of the graph Laplacian-matrix combined with hierarchical-clustering techniques, and…
We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of…
With invaluable theoretical and practical benefits, the problem of partitioning networks for community structures has attracted significant research attention in scientific and engineering disciplines. In literature, Newman's modularity…
Many real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network…
One of the most relevant tasks in network analysis is the detection of community structures, or clustering. Most popular techniques for community detection are based on the maximization of a quality function called modularity, which in turn…
We study networks that display community structure -- groups of nodes within which connections are unusually dense. Using methods from random matrix theory, we calculate the spectra of such networks in the limit of large size, and hence…
In this paper, we first discuss the definition of modularity (Q) used as a metric for community quality and then we review the modularity maximization approaches which were used for community detection in the last decade. Then, we discuss…
Community detection is a fundamental network-analysis primitive with a variety of applications in diverse domains. Although the modularity introduced by Newman and Girvan (2004) has widely been used as a quality function for community…
Community structures detection is one of the fundamental problems in complex network analysis towards understanding the topology structures of the network and the functions of it. Nonnegative matrix factorization (NMF) is a widely used…
Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted…
Using an intuitive concept of what constitutes a meaningful community, a novel metric is formulated for detecting non-overlapping communities in undirected, weighted heterogeneous networks. This metric, modularity density, is shown to be…
In this paper, we consider the community detection problem under either the stochastic block model (SBM) assumption or the degree-correlated stochastic block model (DCSBM) assumption. The modularity maximization formulation for the…
Community detection in networks is the process of identifying unusually well-connected sub-networks and is a central component of many applied network analyses. The paradigm of modularity optimization stipulates a partition of the network's…
Communities are clusters of nodes with a higher than average density of internal connections. Their detection is of great relevance to better understand the structure and hierarchies present in a network. Modularity has become a standard…
Community detection in network analysis aims at partitioning nodes in a network into $K$ disjoint communities. Most currently available algorithms assume that $K$ is known, but choosing a correct $K$ is generally very difficult for real…
A "quantitative function" for community detection called modularity density has been proposed by Li, Zhang, Wang, Zhang, and Chen in $[$Phys. Rev. E 77, 036109 (2008)$]$. We study the modularity density maximization problem and we discuss…
Modularity maximization has been one of the most widely used approaches in the last decade for discovering community structure in networks of practical interest in biology, computing, social science, statistical mechanics, and more.…
Modularity maximization is one of the state-of-the-art methods for community detection that has gained popularity in the last decade. Yet it suffers from the resolution limit problem by preferring under certain conditions large communities…
Maximizing the modularity of a network is a successful tool to identify an important community of nodes. However, this combinatorial optimization problem is known to be NP-complete. Inspired by recent nonlinear modularity eigenvector…