Community Detection In Complex Networks Research Articles

Fuzzy clustering with Barber modularity regularization

In this paper, we propose a new algorithm for the joint clustering of two sets of statistical units N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}$$\\end{document} and M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {M}$$\\end{document} which are also equipped with an adjacency structure which is represented by a bipartite network. Our model is based on the fuzzy Partition Around Medoids, and it combines it with techniques for community detection in bipartite complex networks based on Barber modularity maximization. The goal is to produce a partition of N∪M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}\\cup \\mathcal {M}$$\\end{document} into clusters, each of which is also identified by two medoids, one in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}$$\\end{document} and one in M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {M}$$\\end{document}, which represent the typical units in the cluster for each set. Such clusters are optimized so that units in the same cluster both have similar values on their attributes and are likely to be adjacent. We test the algorithm on both simulated and real data, to show how it is able to capture a wide range of different interactions between the distribution of the attributes and the network structure.

An Improved Continuous-Encoding-Based Multiobjective Evolutionary Algorithm for Community Detection in Complex Networks

An Improved Continuous-Encoding-Based Multiobjective Evolutionary Algorithm for Community Detection in Complex Networks

Community structure of tropics emerging from spatio-temporal variations in the Intertropical Convergence Zone dynamics

The Intertropical Convergence Zone (ITCZ) is a narrow tropical belt of deep convective clouds, intense precipitation, and monsoon circulations encircling the Earth. Complex interactions between the ITCZ and local geophysical dynamics result in high climate variability, making weather forecasting and prediction of extreme rainfall or drought events challenging. We unravel the complex spatio-temporal dynamics of the ITCZ and the resulting teleconnection patterns via a novel tropical climate classification achieved using complex network analysis and community detection. We reduce the high-dimensional complex ITCZ dynamics into a simple yet insightful community structure that classifies the tropics into seven regions representing distinct ITCZ dynamics. The two largest communities, encompassing landmasses over the Northern and Southern hemispheres, are associated with coherent seasonal ITCZ dynamics and have significant long-range connections. Temporal analysis of the community structure highlights that the tropical Pacific and Atlantic Oceans communities exhibit substantial variation on multidecadal scales. Further, these communities exhibit incoherent dynamics due to atmosphere-ocean interactions driven by equatorial and coastal oceanic upwelling.

Gain and Pain in Graph Partitioning: Finding Accurate Communities in Complex Networks

This paper presents an approach to community detection in complex networks by simultaneously incorporating a connectivity-based metric and Max-Min Modularity. By leveraging the connectivity-based metric and employing a heuristic algorithm, we develop a novel complementary graph for the Max-Min Modularity that enhances its effectiveness. We formulate community detection as an integer programming problem of an equivalent yet more compact counterpart model of the revised Max-Min Modularity maximization problem. Using a row generation technique alongside the heuristic approach, we then provide a hybrid procedure for near-optimally solving the model and discovering high-quality communities. Through a series of experiments, we demonstrate the success of our algorithm, showcasing its efficiency in detecting communities, particularly in extensive networks.

A Multi-Objective Pigeon-Inspired Optimization Algorithm for Community Detection in Complex Networks

Community structure is a very interesting attribute and feature in complex networks, which has attracted scholars’ attention and research on community detection. Many single-objective optimization algorithms have been migrated and modified to serve community detection problems. Due to the limitation of resolution, the final algorithm implementation effect is not ideal. In this paper, a multi-objective community detection method based on a pigeon-inspired optimization algorithm, MOPIO-Net, is proposed. Firstly, the PIO algorithm is discretized in terms of the solution space representation, position, and velocity-updating strategies to adapt to discrete community detection scenarios. Secondly, by minimizing the two objective functions of community score and community fitness at the same time, the community structure with a tight interior and sparse exterior is obtained. Finally, for the misclassification caused by boundary nodes, a mutation strategy is added to improve the accuracy of the final community recognition. Experiments on synthetic and real networks verify that the proposed algorithm is more accurate in community recognition compared to 11 benchmark algorithms, confirming the effectiveness of the proposed method.

Survey on graph neural network-based community detection and its applications

Detecting communities within a network is a critical component of network analysis. The process involves identifying clusters of nodes that exhibit greater similarity to each other compared to other nodes in the network. In the context of Complex networks (CN), community detection becomes even more important as these clusters provide relevant information of interest. Traditional mathematical and clustering methods have limitations in terms of data visualization and high-dimensional information extraction. To address these challenges, graph neural network learning methods have gained popularity in community detection, as they are capable of handling complex structures and multi-dimensional data. Developing a framework for community detection in complex networks using graph neural network learning is a challenging and ongoing research objective. Therefore, it is essential for researchers to conduct a thorough review of community detection techniques that utilize cutting-edge graph neural network learning methods [102], in order to analyze and construct effective detection models. This paper provides a brief overview of graph neural network learning methods based on community detection methods and summarizes datasets, evaluation metrics, applications, and challenges of community detection in complex networks.

Quantum algorithms for community detection and their empirical run-times

We apply recent work~\cite{ourotherpaper} on empirical estimates of quantum speedups to the practical task of community detection in complex networks. We design several quantum variants of a popular classical algorithm -- the \textit{Louvain algorithm} for community detection -- and first study their complexities in the usual way, before analysing their complexities empirically across a variety of artificial and real inputs. We find that this analysis yields insights not available to us via the asymptotic analysis, further emphasising the utility in such an empirical approach. In particular, we observe that a complicated quantum algorithm with a large asymptotic speedup might not be the fastest algorithm in practice, and that a simple quantum algorithm with a modest speedup might in fact be the one that performs best. Moreover, we repeatedly find that overheads such as those arising from the need to amplify the success probabilities of quantum sub-routines such as Grover search can nullify any speedup that might have been suggested by a theoretical worst- or expected-case analysis.

A motif-based probabilistic approach for community detection in complex networks

Community detection in complex networks is an important task for discovering hidden information in network analysis. Neighborhood density between nodes is one of the fundamental indicators of community presence in the network. A community with a high edge density will have correlations between nodes that extend beyond their immediate neighbors, denoted by motifs. Motifs are repetitive patterns of edges observed with high frequency in the network. We proposed the PCDMS method (Probabilistic Community Detection with Motif Structure) that detects communities by estimating the triangular motif in the network. This study employs structural density between nodes, a key concept in graph analysis. The proposed model has the advantage of using a probabilistic generative model that calculates the latent parameters of the probabilistic model and determines the community based on the likelihood of triangular motifs. The relationship between observing two pairs of nodes in multiple communities leads to an increasing likelihood estimation of the existence of a motif structure between them. The output of the proposed model is the intensity of each node in the communities. The efficiency and validity of the proposed method are evaluated through experimental work on both synthetic and real-world networks; the findings will show that the community identified by the proposed method is more accurate and dense than other algorithms with modularity, NMI, and F1score evaluation metrics.

Semi-supervised community detection method based on generative adversarial networks

Community detection in complex networks often suffers from insufficient data and limited utilization of prior knowledge. In this paper we propose “Semi-supervised Generative Adversarial Network” (GANSE), a novel algorithm that integrates Generative Adversarial Networks (GANs) and semi-supervised learning to address these challenges. This method addresses the issues above through a multi-step process. Initially, the network is rewired using vertex similarity metrics, thereby enhancing its structural integrity. Subsequently, a novel generative adversarial network model is designed, and our model facilitates the reconstruction of the network, thereby yielding partitions. Which form the basis for identifying core communities. Additionally, the local clustering coefficient is incorporated as a reward signal and injected into the node selection process. Moreover, isolated nodes are reallocated, ultimately culminating in the derivation of the final community structure. Experimental results on four large real-life datasets demonstrate the clear superiority of the proposed algorithm in terms of F1 and Jaccard metrics when compared to existing algorithms. Notably, our GANSE method outperforms the traditional algorithms in networks with “missing data”. Thus showing its robustness and effectiveness in real-world incomplete datasets. Our findings highlight the potential of GANs and semi-supervised learning for enhancing community detection accuracy in complex networks.

A Node Classification-Based Multiobjective Evolutionary Algorithm for Community Detection in Complex Networks

Multiobjective evolutionary algorithms (MOEAs) have been widely used in community detection in recent years. However, most of the existing MOEA-based ones adopted the same search strategies for all nodes and ignored the differences between the nodes. In fact, the nodes in a complex network have different structural characteristics and are of different importance during the search process of the community detection problem. To this end, in this article, a node classification-based search scheme is first proposed, where different kinds of nodes are searched in different ways. To be specific, the nodes in the network are classified into two types of nodes, candidate central (CC) nodes and noncentral (NC) nodes, by mapping the nodes into a structural similarity-based embedding space. The CC nodes are likely to be the centers of communities, and the rough structure can be searched quickly through activating the CC nodes. Then, the NC nodes are assigned to the communities with the activated central nodes. Based on the proposed scheme, a node classification-based MOEA named NCMOEA is then proposed. In NCMOEA, a mixed representation is designed to effectively encode the two different kinds of nodes. In addition, corresponding genetic operators are then suggested to search the two categories of nodes in different ways. Furthermore, an initialization strategy is also designed for initializing the population with high quality and good diversity. The experimental results on 15 real-world networks and several synthetic networks demonstrate the superiority of the proposed NCMOEA over nine representative algorithms for community detection.

Robust Overlapping Community Detection in Complex Networks With Graph Convolutional Networks and Fuzzy C-Means

Robust Overlapping Community Detection in Complex Networks With Graph Convolutional Networks and Fuzzy C-Means

Towards improving community detection in complex networks using influential nodes

Abstract Complex network analysis is inspired by empirical studies of real-world networks such as computer networks, technology networks and social networks. The analysis of community structure in complex networks is understood as an important issue by the research society. A community is a set of nodes in a network where the density of connections is high. The insight in the literature shows many approaches to identify influential nodes, but these approaches only lead to finding community centres. Meanwhile, clustering techniques are effectively used for community detection, where they can reveal group structure and hidden connections by considering topological and demographic information. This article presents an ensemble clustering algorithm based on influential nodes to improve community detection in complex networks. Considering different characteristics of the network, the proposed method seeks to discover common interests between users and their behaviours to identify the most suitable communities. First, a set of influential nodes are identified as community centres. Then, these centres are considered as cluster centres. After that, primary clusters are created based on the determined centres. Finally, the primary clusters are reclustered to form the final clusters. Here, the final clusters are considered as communities of users in the network. The simulation has been performed on real-world networks and the results confirm the effectiveness of the proposed method. Specifically, the communities identified by the proposed method are 2.1% better than the best existing state-of-the-art method in terms of modularity. Keywords: complex network; community detection; influential nodes; ensemble clustering.

Higher-order interactions disturb community detection in complex networks

Edges are the most basic structures in complex networks, representing relationships of node pairs. However, many higher-order interactions in reality are beyond node-to-node relationships. In recent years, the conceptualization of “higher-order structures” is considered to provide information on multiple scales, which is helpful to discover new conclusions or achieve better results in issues such as propagation, synchronization, and evolution. But for community identification, the impact of higher-order interactions may not be positive. In this study, we discovered that higher-order interactions disproportionately increase the count of edges. This poses a substantial challenge for community detection, especially when we found that higher-order interactions tend to cross multiple communities. The existence of higher-order interactions obscures the community structure in the network. And once we realize this, removing some of the higher-order interactions is an easy way to improve the accuracy of community detection.

Overlapping community detection in software ecosystem based on pheromone guided personalized PageRank algorithm

Software ecosystem has aroused the interest of numerous researchers and plays an important role in many aspects. According to different participants and their relationships, software ecosystem can be constructed into various types of complex networks. Overlapping community detection in complex networks can help reveal the community structure and find the intersection between communities. However, existing overlapping community detection algorithms often suffer from reduced applicability or accuracy when applied to networks in software ecosystems. To reveal the overlapping community structure in software ecosystem, we propose an overlapping community detection algorithm by improving the standard personalized PageRank (PPR) algorithm. We first construct a developer collaboration network in software ecosystem based on the intensity of cooperation between developers. Then, the similarity between developers is calculated to guide the walking process of the PPR algorithm, making it suitable for weighted networks. Finally, in the proposed algorithm PGPPR, inspired by the idea of using pheromones to guide the walking in ant colony algorithm, we run the algorithm in multiple rounds and use the results of the previous round to guide the walking process in the current round to reduce redundant diffusion. The experimental results on the five real-world networks show that our algorithm is applicable and effective in detecting communities. And in the five developer collaboration networks, PGPPR can effectively detect overlapping community structures with higher stability and accuracy than the four baselines. The PGPPR algorithm can find overlapping community structures in weighted networks and effectively reduce the redundant diffusion generated when applying the standard PPR algorithm to community detection. Compared to other algorithms, our algorithm can detect the overlapping communities more accurately and stably when applied to developer collaboration networks in software ecosystem.

Unsupervised Community Detection Algorithm with Stochastic Competitive Learning Incorporating Local Node Similarity

Community detection is an important task in the analysis of complex networks, which is significant for mining and analyzing the organization and function of networks. As an unsupervised learning algorithm based on the particle competition mechanism, stochastic competitive learning has been applied in the field of community detection in complex networks, but still has several limitations. In order to improve the stability and accuracy of stochastic competitive learning and solve the problem of community detection, we propose an unsupervised community detection algorithm LNSSCL (Local Node Similarity-Integrated Stochastic Competitive Learning). The algorithm calculates node degree as well as Salton similarity metrics to determine the starting position of particle walk; local node similarity is incorporated into the particle preferential walk rule; the particle is dynamically adjusted to control capability increments according to the control range; particles select the node with the strongest control capability within the node to be resurrected; and the LNSSCL algorithm introduces a node affiliation selection step to adjust the node community labels. Experimental comparisons with 12 representative community detection algorithms on real network datasets and synthetic networks show that the LNSSCL algorithm is overall better than other compared algorithms in terms of standardized mutual information (NMI) and modularity (Q). The improvement effect for the stochastic competition learning algorithm is evident, and it can effectively accomplish the community detection task in complex networks.

Community Detection in Modular Complex Networks Using an Improved Particle Swarm Optimization Algorithm

Community detection is an important and interesting topic for better understanding and analyzing complex network structures. Detecting hidden partitions in complex networks is proven to be an NP-hard problem that may not be accurately resolved using traditional methods. So it is solved using evolutionary computation methods and modeled in the literature as an optimization problem. In recent years, many researchers have directed their research efforts toward addressing the problem of community structure detection by developing different algorithms and making use of single-objective optimization methods. In this study, we have continued that research line by improving the Particle Swarm Optimization (PSO) algorithm using a local improvement operator to effectively discover community structure in the modular complex networks when employing the modularity density metric as a single-objective function. The framework of the proposed algorithm consists of three main steps: an initialization strategy, a movement strategy based on perturbation genetic operators, and an improvement operator. The key idea behind the improvement operator is to determine and reassign the complex network nodes that are located in the wrong communities if the majority of their topological links do not belong to their current communities, making it appear that these nodes belong to another community. The performance of the proposed algorithm has been tested and evaluated when applied to publicly-available modular complex networks generated using a flexible and simple benchmark generator. The experimental results showed the effectiveness of the suggested method in discovering community structure over modular networks of different complexities and sizes.

Density-Based Entropy Centrality for Community Detection in Complex Networks.

One of the most important problems in complex networks is the location of nodes that are essential or play a main role in the network. Nodes with main local roles are the centers of real communities. Communities are sets of nodes of complex networks and are densely connected internally. Choosing the right nodes as seeds of the communities is crucial in determining real communities. We propose a new centrality measure named density-based entropy centrality for the local identification of the most important nodes. It measures the entropy of the sum of the sizes of the maximal cliques to which each node and its neighbor nodes belong. The proposed centrality is a local measure for explaining the local influence of each node, which provides an efficient way to locally identify the most important nodes and for community detection because communities are local structures. It can be computed independently for individual vertices, for large networks, and for not well-specified networks. The use of the proposed density-based entropy centrality for community seed selection and community detection outperforms other centrality measures.

A Macro-Micro Population-Based Co-Evolutionary Multi-Objective Algorithm for Community Detection in Complex Networks [Research Frontier

A Macro-Micro Population-Based Co-Evolutionary Multi-Objective Algorithm for Community Detection in Complex Networks [Research Frontier

GLOD: The Local Greedy Expansion Method for Overlapping Community Detection in Dynamic Provenance Networks

Local overlapping community detection is a hot problem in the field of studying complex networks. It is the process of finding dense clusters based on local network information. This paper proposes a method called local greedy extended dynamic overlapping community detection (GLOD) to address the challenges of detecting high-quality overlapping communities in complex networks. The goal is to improve the accuracy of community detection by considering the dynamic nature of community boundaries and leveraging local network information. The GLOD method consists of several steps. First, a coupling seed is constructed by selecting nodes from blank communities (i.e., nodes not assigned to any community) and their similar neighboring nodes. This seed serves as the starting point for community detection. Next, the seed boundaries are extended by applying multiple community fitness functions. These fitness functions determine the likelihood of nodes belonging to a specific community based on various local network properties. By iteratively expanding the seed boundaries, communities with higher density and better internal structure are formed. Finally, the overlapping communities are merged using an improved version of the Jaccard coefficient, which is a measure of similarity between sets. This step ensures that overlapping nodes between communities are properly identified and accounted for in the final community structure. The proposed method is evaluated using real networks and three sets of LFR (Lancichinetti–Fortunato–Radicchi) networks, which are synthetic benchmark networks widely used in community detection research. The experimental results demonstrate that GLOD outperforms existing algorithms and achieves a 2.1% improvement in the F-score, a community quality evaluation metric, compared to the LOCD framework. It outperforms the best existing LOCD algorithm on the real provenance network. In summary, the GLOD method aims to overcome the limitations of existing community detection algorithms by incorporating local network information, considering overlapping communities, and dynamically adjusting community boundaries. The experimental results suggest that GLOD is effective in improving the quality of community detection in complex networks.

A Two-Stage Multi-Objective Evolutionary Algorithm for Community Detection in Complex Networks

Community detection is a crucial research direction in the analysis of complex networks and has been shown to be an NP-hard problem (a problem that is at least as hard as the hardest problems in nondeterministic polynomial time). Multi-objective evolutionary algorithms (MOEAs) have demonstrated promising performance in community detection. Given that distinct crossover operators are suitable for various stages of algorithm evolution, we propose a two-stage algorithm that uses an individual similarity parameter to divide the algorithm into two stages. We employ appropriate crossover operators for each stage to achieve optimal performance. Additionally, a repair operation is applied to boundary-independent nodes during the second phase of the algorithm, resulting in improved community partitioning results. We assessed the effectiveness of the algorithm by measuring its performance on a synthetic network and four real-world network datasets. Compared to four existing competing methods, our algorithm achieves better accuracy and stability.