Overlapping community detection in complex networks using fuzzy theory, balanced link density, and label propagation

Community detection in complex networks has increasingly become an important topic in the network, but in most community detection methods, a single node only belongs to one community. In fact, there is often overlap among real-world online communities. In this paper, an overlapping community detection algorithm based on subgraph structure and multi-optimization method is designed. In this algorithm, the maximum clique mined by k-core decomposition is used as the clique node, thus the overlap characteristic is transformed into the inherent characteristic of the new graph. After that, a population initialization method based on k-core decomposition is designed, and the discrete framework of multi-objective particle swarm optimization algorithm is used to optimize the two objectives on the basis of maximal clique graph to solve the problem of overlapping community detection. In the real-world network, this algorithm is compared with similar community detection algorithms. The comparison of the evaluation indexe shows that the community detection effect of this algorithm is similar to that of similar algorithms, and has a good application prospect.

With the rapid increase in popularity of online social networks, community detection in these networks has become a key aspect of research field. Overlapping community detection is an important NP-hard problem of social network analysis. Modularity-based community detection is one of the most widely used approaches for social network analysis. However, modularity-based community detection technique may fail to resolve small-size communities. Hence, we propose a novel two-step approach for overlapping community detection in social networks. In the first step, modularity density-based hybrid meta-heuristics approach is used to find the disjoint communities and the quality of these disjoint communities can be verified using Silhouette coefficient. In the second step, the quality disjoint communities with low computation cost are used to detect overlapping nodes based on Min-Max Ratio of minimum(indegree, outdegree) to the maximum(indegree, outdegree) values of nodes. We tested the proposed algorithm based on 10 standard community quality metrics along with Silhouette score using seven standard datasets. Experimental results demonstrate that the proposed approach outperforms the current state-of-the-art works in terms of quality and scalability.

There is an increasing recognition on community detection in complex networks in recent years. In this study, we improve a recently proposed memetic algorithm for community detection in networks. By introducing a Population Generation via Label Propagation (PGLP) tactic, an Elitism Strategy (ES) and an Improved Simulated Annealing Combined Local Search (ISACLS) strategy, the improved memetic algorithm called (iMeme-Net) is put forward for solving community detection problems. Experiments on both computer-generated and real-world networks show the effectiveness and the multi-resolution ability of the proposed method.

Community detection is of extraordinary significance in comprehending the structure and functions of complex networks. The particle competition algorithm is a quick and heuristic algorithm when applied to community detection. However, existing particle competition algorithms do not make full use of all information of networks and have several shortcomings such as poor robustness, weak stability, and low accuracy. In addition, it cannot be effectively applied to overlapping community detection. In this paper, a new particle propagation model with semi-supervised learning for community detection in social networks (SSPCO) is proposed. SSPCO divides the formation process of communities into the initialization phase, walking phase, restart phase, convergence phase and overlapping community detection phase. In the initialization phase, each team of labeled vertices generates a particle of this team. The domination level of each team particles at vertices and edges is also initialized in this phase. In the walking phase, the particle walks to one of the neighbors of the current vertex based on the proposed walking probability calculated by the proposed transfer acceptance probability and the proposed transfer proposal probability. In the process of particle walking, the particle has a possibility of entering the restart phase. The proposed restart probability determines whether the particle performs the restart mechanism. If the particle decides to restart, it will select a vertex for restart based on the domination level of this team particles at vertices. Otherwise, it continues to walk. After several particle walking and restart phases, the particle meets the convergence state. In the convergence phase, if all particles meet the proposed convergence condition, we will obtain community partition results based on the domination level of each team particles at the vertex. In the overlapping community detection phase, we can obtain overlapping community partition results based on the overlapping community detection mechanism. Experiment results reveal that SSPCO can improve the stability and accuracy of detecting communities. Moreover, SSPCO runs in near-linear time complexity, which allows it to be applied in large-sized networks.

Community structure is an important feature of a complex network, where detection of the community structure can shed some light on the properties of such a complex network. Amongst the proposed community detection methods, the label propagation algorithm (LPA) emerges as an effective detection method due to its time efficiency. Despite this advantage in computational time, the performance of LPA is affected by randomness in the algorithm. A modified LPA, called CLPA-GNR, was proposed recently and it succeeded in handling the randomness issues in the LPA. However, it did not remove the tendency for trivial detection in networks with a weak community structure. In this paper, an improved CLPA-GNR is therefore proposed. In the new algorithm, the unassigned and assigned nodes are updated synchronously while the assigned nodes are updated asynchronously. A similarity score, based on the Sørensen-Dice index, is implemented to detect the initial communities and for breaking ties during the propagation process. Constraints are utilised during the label propagation and community merging processes. The performance of the proposed algorithm is evaluated on various benchmark and real-world networks. We find that it is able to avoid trivial detection while showing substantial improvement in the quality of detection.

Traditional community detection methods in attributed networks (eg, social network) usually disregard abundant node attribute information and only focus on structural information of a graph. Existing community detection methods in attributed networks are mostly applied in the detection of nonoverlapping communities and cannot be directly used to detect the overlapping structures. This article proposes an overlapping community detection algorithm in attributed networks. First, we employ the modified X‐means algorithm to cluster attributes to form different themes. Second, we employ the label propagation algorithm (LPA), which is based on neighborhood network conductance for priority and the rule of theme weight, to detect communities in each theme. Finally, we perform redundant processing to form the final community division. The proposed algorithm improves the X‐means algorithm to avoid the effects of outliers. Problems of LPA such as instability of division and adjacent communities being easily merged can be corrected by prioritizing the node neighborhood network conductance. As the community is detected in the attribute subspace, the algorithm can find overlapping communities. Experimental results on real‐attributed and synthetic‐attributed networks show that the performance of the proposed algorithm is excellent with multiple evaluation metrics.

Communities are virtually ubiquitous in real-world networks, and the statistic of modularity index Q is the classical measurement for community detection algorithms. However, the relationship between the modularity property and network multilever micro-scale structures is still not clear. In this paper, we study community detection results both in artificial and real-life complex networks by constructing different order null networks, and the results uncover that how micro-structures (such as degree distribution, assortativity and clustering coefficient) affect community properties. Meanwhile, we also propose two novel null networks (increasing or decreasing community structures) to verify the robustness of different community detection algorithms. Our results indicate that the modularity index Q is not a suitable statistic to measure the weak community property which is widely available in empirical networks. Our findings can not only be used to test the robustness of different community detection methods, but also be helpful to uncover the correlation of network structures between microcosmic and mesoscopic scales.

Communities are basic units of complex networks and understanding of their structure help us to understand the structure of a network. Communities are groups of nodes that have many links inside and few links outside them. Community detection in a network can be modeled as an optimization problem. We can use some measures such as Modularity and Community Score for evaluating the quality of a partition of nodes. In this paper, we present a new algorithm for detecting communities in networks based on an Estimation of Distribution Algorithm (EDA) with the assumption that the problem variables are independent. EDAs are those evolutionary algorithms that build and sample the probabilistic models of selected solutions instead of using crossover and mutation operators. In this paper, we assess our algorithm by synthetic and real data sets and compare it with other community detection algorithms.

Social networks are ubiquitous in our daily life. Due to the rapid development of information and electronic technology, social networks are becoming more and more complex in terms of sizes and contents. It is of paramount significance to analyse the structures of social networks in order to unveil the myth beneath complex social networks. Network community detection is recognised as a fundamental tool towards social networks analytics. As a consequence, numerical community detection methods are proposed in the literature. For a real-world social network, an individual may possess multiple memberships, while the existing community detection methods are mainly designed for non-overlapping situations. With regard to this, this paper proposes a hybrid metaheuristic method to detect overlapping communities in social networks. In the proposed method, the overlapping community detection problem is formulated as an optimisation problem and a novel bat optimisation algorithm is designed to solve the established optimisation model. To enhance the searchability of the proposed algorithm, a local search operator based on tabu search is introduced. To validate the effectiveness of the proposed algorithm, experiments on benchmark and real-world social networks are carried out. The experiments indicate that the proposed algorithm is promising for overlapping community detection.

The problem of community detection is relevant in many disciplines of science and modularity optimization is the widely accepted method for this purpose. It has recently been shown that this approach presents a resolution limit by which it is not possible to detect communities with sizes smaller than a threshold, which depends on the network size. Moreover, it might happen that the communities resulting from such an approach do not satisfy the usual qualitative definition of commune; i.e., nodes in a commune are more connected among themselves than to nodes outside the commune. In this paper we present a different method for community detection in complex networks. We define merit factors based on the weak and strong community definitions formulated by Radicchi [Proc. Natl. Acad. Sci. U.S.A. 101, 2658 (2004)] and we show that these local definitions avoid the resolution limit problem found in the modularity optimization approach.

Community detection in complex networks is an important multidisciplinary research area and is considered crucial for understanding the structure of complex networks. Unsupervised deep learning models (e.g. stack autoencoders) have been successfully proposed for the problem of community detection, which can extract network features and use them in splitting the network into communities. Despite their effectiveness, these methods are not very efficient, especially when large networks are involved. Furthermore, existing models usually handle the network as a single object, which means that massive trainable parameters are required during training (which in normal complex networks often reach millions of parameters, not to mention large networks), thereby increasing the complexity of the model. To overcome these problems, this paper proposes a deep autoencoder method for network community detection based on three techniques: network-data partitioning, reduction and sharing of trainable parameters, which contribute significantly to improve the efficiency of the method. A new partitioning strategy is imposed on complex networks at different levels. The paper also proposes a parallel design for the proposed method. Furthermore, a new similarity constraint function is proposed to improve and preserve the performance of community detection task. We performed extensive experiments for different partitioning levels of a network-dataset to evaluate the method with CPU and GPU devices. The results showed that the proposed method significantly improved training speed and efficiency while maintaining performance. The results also showed that the efficiency of the method increases as we move to a deeper level of partitioning.

Label propagation algorithm (LPA) has been proven to be an extremely fast method for community detection in large complex networks. But an important issue of the algorithm has not yet been properly addressed that random update orders in label propagation process hamper the algorithm robustness of algorithm. We note that when there are multiple maximal labels among a node neighbors' labels, choosing a node' label from which there is a local cycle to the node instead of a random node' label can avoid the labels propagating among communities at random. In this paper, an improved LPA based on local cycles is given. We have evaluated the proposed algorithm on computer-generated networks with planted partition and some real-world networks whose community structure are already known. The result shows that the performance of the proposed approach is even significantly improved.

<p dir="ltr">One of the most critical features of real-world networks is their community structure, as it reveals the internal organization of nodes. Finding such partitions is an interesting and essential task from both theoretical and practical perspectives. As a result, there is a growing demand for effective community detection algorithms. However, testing and designing such algorithms is demanding and challenging: one of the biggest problems is the lack of proper datasets and the fact that some have disputable ground-truth labeling, to say the least. One way to avoid this problem is to use artificial benchmarks with a built-in community structure.</p><p dir="ltr">In this work, we propose ABCDe—a multi-threaded implementation of the ABCD (Artificial Benchmark for Community Detection) graph generator. We test its performance and compare it with the previously available sequential version of the ABCD model and the parallel implementation of the standard and widely used LFR generator. We also investigate various theoretical asymptotic properties of the ABCD and ABCDe models. In particular, we analyze the modularity function, arguably the most important graph property in the context of community detection. By doing so, we show that models from the ABCD family are proper tools for designing new algorithms, not only those suited specifically for the community detection task.</p><p dir="ltr">Finally, we introduce a new approach to community detection in graphs. The idea is to initialize one of the popular heuristic-based community detection algorithms, such as Louvain or Leiden, with a partition obtained by embedding the graph nodes into a high-dimensional real vector space and then running a clustering algorithm on this latent representation. This procedure significantly improves the results and reduces the inherent volatility of such algorithms. Proper embedding filters out unnecessary information while retaining the proximity of nodes belonging to the same community.</p>

Complex networks (CNs) have gained much attention in recent years due to their importance and popularity. The rapid growth in the size of CNs leads to more difficulties in the analysis of CNs tasks. Community Detection (CD) is an important multidisciplinary research area where many machine/deep learning-based methods have been applied to map CNs into a low-dimensional representation for extracting information similarity among members of CNs. Currently, Deep Learning (DL) is one of the promising methods to extract knowledge and learn information from high dimensional space and represent it in low dimensional space. However, designing an accurate and efficient DL-based CD method especially when dealing with large CNs is always an on-going research endeavor to pursue. Meta-Heuristic (MH) algorithms have shown their potentials in improving DL models in terms of solution quality and computational cost. In addition, parallel computing is a feasible solution for building efficient DL models. The algorithmic principle of MH is parallel in nature; however, its computation framework in DL training that is reported in the literature is not really implemented in a parallel computing setup. In this paper, we present a systematic review of CD in CNs from conventional machine learning to DL methods and point out the gap of applying DL-based CD methods in large CNs. In addition, the relevant studies on DL with parallel and MH approaches are reviewed and their implications on DL models are highlighted to prospect effective solutions to overcome the challenges of DL-based CD methods. We also point out research challenges in the field of CD and suggest possible future research directions.

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.