Detecting Community Structure Research Articles

Two-sample test for stochastic block models via the largest singular value

The stochastic block model is widely used for detecting community structures in network data. However, the research interest in much of the literature focuses on the study of one sample of stochastic block models. Detecting the difference between the two community structures is a less studied issue for stochastic block models. In this article, we propose a novel test statistic based on the largest singular value of a residual matrix obtained by subtracting the geometric mean of two estimated block mean effects from the sum of two observed adjacency matrices. We prove that the null distribution of the proposed test statistic converges in distribution to the Tracy-Widom distribution with index 1, and we show the difference between the two samples for stochastic block models can be tested via the proposed method. We show that the proposed test is asymptotically powerful against alternative models. Further, we extend the proposed method to the degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.

An Algorithm Based on Non-Negative Matrix Factorization for Detecting Communities in Networks

Community structure is a significant characteristic of complex networks, and community detection has valuable applications in network structure analysis. Non-negative matrix factorization (NMF) is a key set of algorithms used to solve the community detection issue. Nevertheless, the localization of feature vectors in the adjacency matrix, which represents the characteristics of complex network structures, frequently leads to the failure of NMF-based approaches when the data matrix has a low density. This paper presents a novel algorithm for detecting sparse network communities using non-negative matrix factorization (NMF). The algorithm utilizes local feature vectors to represent the original network topological features and learns regularization matrices. The resulting feature matrices effectively reveal the global structure of the data matrix, demonstrating enhanced feature expression capabilities. The regularized data matrix resolves the issue of localized feature vectors caused by sparsity or noise, in contrast to the adjacency matrix. The approach has superior accuracy in detecting community structures compared to standard NMF-based community detection algorithms, as evidenced by experimental findings on both simulated and real-world networks.

Bayesian inference of financial networks

Network data arises naturally in a wide variety of applications in different fields. In this article we discuss in detail the statistical modeling of financial networks. The structure of such networks red has not been studied thoroughly in the past, mainly due to limited accessible data. We explore the structure of a real trading network corresponding to transactions within the natural gas future market over a four-year period. The detection of meaningful communities of actors within networks is particularly relevant to understand the topology of a complex system like this. We explore the usage of stochastic block models in conjunction with a nonparametric Bayesian approach in order to identify clusters of traders in a flexible modeling framework. Our findings strongly indicate that the proposed models are highly reliable at detecting community structures.

Improved brain community structure detection by two-step weighted modularity maximization

The human brain can be regarded as a complex network with interacting connections between brain regions. Complex brain network analyses have been widely applied to functional magnetic resonance imaging (fMRI) data and have revealed the existence of community structures in brain networks. The identification of communities may provide insight into understanding the topological functions of brain networks. Among various community detection methods, the modularity maximization (MM) method has the advantages of model conciseness, fast convergence and strong adaptability to large-scale networks and has been extended from single-layer networks to multilayer networks to investigate the community structure changes of brain networks. However, the problems of MM, suffering from instability and failing to detect hierarchical community structure in networks, largely limit the application of MM in the community detection of brain networks. In this study, we proposed the weighted modularity maximization (WMM) method by using the weight matrix to weight the adjacency matrix and improve the performance of MM. Moreover, we further proposed the two-step WMM method to detect the hierarchical community structures of networks by utilizing node attributes. The results of the synthetic networks without node attributes demonstrated that WMM showed better partition accuracy than both MM and robust MM and better stability than MM. The two-step WMM method showed better accuracy of community partitioning than WMM for synthetic networks with node attributes. Moreover, the results of resting state fMRI (rs-fMRI) data showed that two-step WMM had the advantage of detecting the hierarchical communities over WMM and was more insensitive to the density of the rs-fMRI networks than WMM.

A Hybrid Probabilistic Privacy Preserving Based Community Detection Model on Online Social Networking Data

Privacy preserving plays a vital role on the online social networking sites due to high dimensionality and data size. Community detection is used to find the social relationships among the node edges and links. However, most of the conventional models are difficult to process the community structure detection due to high computational time and memory. Also, these models require contextual weighted nodes information for privacy preserving process. In order to overcome these issues, an advanced probabilistic weighted based community detection and privacy preserving framework is developed on the large social networking data. In this model, a filter based probabilistic model is developed to remove the sparse values and to find the weighted community detection nodes and its profiles for privacy preserving process. Experimental results show that the filter based probabilistic community detection framework has better efficiency in terms of normalized mutual information, Q, rand index and runtime (ms).

CDBRA: Community Detection Based on Random Algorithm in Social Networks

Understanding the topology and functions of complex networks allows us to derive valuable information from them. There are various types of these networks. Community detection is a significant research area that involves dividing a network graph into subsets of nodes, known as communities. Each community consists of nodes that have dense communication with each other and sparse communication with nodes outside the community. This work proposes the use of Community Detection based on random Algorithm (CDBRA) to identify novel communities with low complexity and high accuracy by using both local and global network information. The proposed method consists of four components: Pre-Processing, Node Identification, Intra-Community Structure, and Inter-Community Structure. In the initial component, the task involves recognizing and saving similarity measures. Additionally, it requires assigning suitable weights to network vertex and edges, taking into the account of local and global network information. The next level involves using a random algorithm enhanced by nodes' weights to determine similarity measures for Node Identification. The third level, Intra-Community Structure, aims to achieve various community structures. The fourth level ultimately chooses the optimal community structure by taking into account the Inter-Community Structure and the evaluation functions derived from network’s local and global information. To assess the proposed method on various scenarios involving real and artificial networks. The proposed method outperforms existing methods in detecting community structures similar to real communities and provides efficient evaluation functions for all types and sizes of 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.

HLEGF: An Effective Hypernetwork Community Detection Algorithm Based on Local Expansion and Global Fusion

Community structure is crucial for understanding network characteristics, and the local expansion method has performed well in detecting community structures. However, there are two problems with this method. Firstly, it can only add nodes or edges on the basis of existing clusters, and secondly, it can produce a large number of small communities. In this paper, we extend the local expansion method based on ordinary graph to hypergraph, and propose an effective hypernetwork community detection algorithm based on local expansion (LE) and global fusion (GF), which is referred to as HLEGF. The LE process obtains multiple small sub-hypergraphs by deleting and adding hyperedges, while the GF process optimizes the sub-hypergraphs generated by the local expansion process. To solve the first problem, the HLEGF algorithm introduces the concepts of community neighborhood and community boundary to delete some nodes and hyperedges in hypergraphs. To solve the second problem, the HLEGF algorithm establishes correlations between adjacent sub-hypergraphs through global fusion. We evaluated the performance of the HLEGF algorithm in the real hypernetwork and six synthetic random hypernetworks with different probabilities. Because the HLEGF algorithm introduces the concepts of community boundary and neighborhood, and the concept of a series of similarities, the algorithm has superiority. In the real hypernetwork, the HLEGF algorithm is consistent with the classical Spectral algorithm, while in the random hypernetwork, when the probability is not less than 0.95, the NMI value of the HLEGF algorithm is always greater than 0.92, and the RI value is always greater than 0.97. When the probability is 0.95, the HLEGF algorithm achieves a 2.3% improvement in the NMI value, compared to the Spectral algorithm. Finally, we applied the HLEGF algorithm to the drug–target hypernetwork to partition drugs with similar functions into communities.

Benchmarking graph representation learning algorithms for detecting modules in molecular networks

Background: A common task in molecular network analysis is the detection of community structures or modules. Such modules are frequently associated with shared biological functions and are often disrupted in disease. Detection of community structure entails clustering nodes in the graph, and many algorithms apply a clustering algorithm on an input node embedding. Graph representation learning offers a powerful framework to learn node embeddings to perform various downstream tasks such as clustering. Deep embedding methods based on graph neural networks can have substantially better performance on machine learning tasks on graphs, including module detection; however, existing studies have focused on social and citation networks. It is currently unclear if deep embedding methods offer any advantage over shallow embedding methods for detecting modules in molecular networks. Methods: Here, we investigated deep and shallow graph representation learning algorithms on synthetic and real cell-type specific gene interaction networks to detect gene modules and identify pathways affected by sequence nucleotide polymorphisms. We used multiple criteria to assess the quality of the clusters based on connectivity as well as overrepresentation of biological processes. Results: On synthetic networks, deep embedding based on a variational graph autoencoder had superior performance as measured by modularity metrics, followed closely by shallow methods, node2vec and Graph Laplacian embedding. However, the performance of the deep methods worsens when the overall connectivity between clusters increases. On real molecular networks, deep embedding methods did not have a clear advantage and the performance depended upon the properties of the graph and the metrics. Conclusions: Deep graph representation learning algorithms for module detection-based tasks can be beneficial for some biological networks, but the performance depends upon the metrics and graph properties. Across different network types, Graph Laplacian embedding followed by node2vec are the best performing algorithms.

A Unified Spectral Clustering Approach for Detecting Community Structure in Multilayer Networks

Networks offer a compact representation of complex systems such as social, communication, and biological systems. Traditional network models are often inadequate to capture the diverse nature of contemporary networks, which may exhibit temporal variation and multiple types of interactions between entities. Multilayer networks (MLNs) provide a more comprehensive representation by allowing interactions between nodes to be represented by different types of links, each reflecting a distinct type of interaction. Community detection reveals meaningful structure and provides a better understanding of the overall functioning of networks. Current approaches to multilayer community detection are either limited to community detection over the aggregated network or are extensions of single-layer community detection methods with simplifying assumptions such as a common community structure across layers. Moreover, most of the existing methods are limited to multiplex networks with no inter-layer edges. In this paper, we introduce a spectral-clustering-based community detection method for two-layer MLNs. The problem of detecting the community structure is formulated as an optimization problem where the normalized cut for each layer is minimized simultaneously with the normalized cut for the bipartite network along with regularization terms that ensure the consistency of the within- and across-layer community structures. The proposed method is evaluated on both synthetic and real networks and compared to state-of-the-art methods. MLNs. The problem of detecting the community structure is formulated as an optimization problem where the normalized cut for each layer is minimized simultaneously with the normalized cut for the bipartite network along with regularization terms that ensure the consistency of the intra- and inter-layer community structures. The proposed method is evaluated on both synthetic and real networks and compared to state-of-the-art methods.

Community detection for weighted bipartite networks

The bipartite network appears in various areas, such as biology, sociology, physiology, and computer science. Rohe et al. (2016) proposed Stochastic co-Blockmodel (ScBM) as a tool for detecting community structure of binary bipartite graph data in network studies. However, ScBM completely ignores edge weight and is unable to explain the block structures of a weighted bipartite network. Here, to model a weighted bipartite network, we introduce a Bipartite Distribution-Free model by releasing ScBM’s distribution restriction. We also build an extension of the proposed model by considering the variation of node degree. Our models do not require a specific distribution on generating elements of the adjacency matrix but only a block structure on the expected adjacency matrix. Spectral algorithms with theoretical guarantees on the consistent estimation of node labels are presented to identify communities. Our proposed methods are illustrated by simulated and empirical examples.

Random search immune algorithm for community detection

Community detection is a prominent research topic in Complex Network Analysis, and it constitutes an important research field on all those areas where complex networks represent a powerful interpretation tool for describing and understanding systems involved in neuroscience, biology, social science, economy, and many others. A challenging approach to uncover the community structure in complex network, and then revealing the internal organization of nodes, is Modularity optimization. In this research paper, we present an immune optimization algorithm (opt-IA) developed to detect community structures, with the main aim to maximize the modularity produced by the discovered communities. In order to assess the performance of opt-IA, we compared it with an overall of 20 heuristics and metaheuristics, among which one Hyper-Heuristic method, using social and biological complex networks as data set. Unlike these algorithms, opt-IA is entirely based on a fully random search process, which in turn is combined with purely stochastic operators. According to the obtained outcomes, opt-IA shows strictly better performances than almost all heuristics and metaheuristics to which it was compared; whilst it turns out to be comparable with the Hyper-Heuristic method. Overall, it can be claimed that opt-IA, even if driven by a purely random process, proves to be reliable and with efficient performance. Furthermore, to prove the latter claim, a sensitivity analysis of the functionality was conducted, using the classic metrics NMI, ARI and NVI.

Multi-Modal Non-Euclidean Brain Network Analysis With Community Detection and Convolutional Autoencoder

Brain network analysis is one of the most effective methods for brain disease diagnosis. Existing studies have shown that exploring information from multimodal data is a valuable way to improve the effectiveness of brain network analysis. In recent years, deep learning has received more and more attention due to its powerful feature learning capabilities, and it is natural to introduce this tool into multi-modal brain networks analysis. However, it would face two challenges. One is that brain network is in non-Euclidean domain, so the convolution kernel in deep learning cannot be directly used to brain networks. The other is that most of existing multi-modal brain network analysis methods cannot extract full use of complementary information from distinct modalities. In this paper, we propose a multi-modal non-Euclidean brain network analysis method based on community detection and convolutional autoencoder, which can solve the above two problems simultaneously in one framework (M2CDCA). First, we construct the functional and structural brain network, respectively. Second, we design a multi-modal interactive community detection method that exploits structural modality to guide functional modality for detecting community structure, then readjusts the nodes distribution so that the adjusted brain network can preserve the potential community information and is more suitable for convolution kernels. Finally, we design a dual-channel autoencoder model with self-attention mechanism to capture hierarchical and highly non-linear features, then comprehensively use two modalities information for classification. We evaluate our method on an epilepsy dataset, the experimental results show that our method outperform several state-of-the-art methods.

Large-scale community detection based on core node and layer-by-layer label propagation

With the vigorous development of big data, the task of large-scale community structure detection is more challenging. In this paper, a large-scale community detection method based on core node and layer-by-layer label propagation is proposed, which is further extended to the detection of overlapping community structures. First, the core nodes whose node degree is greater than the average degree in the graph are found to make effective use of the feature that the core node is the potential community center. This will also avoid the impact of nodes with low node degrees on community structure detection. Then, starting from the core node, label propagation is carried out layer-by-layer according to the node degree and node connection, which effectively improves the accuracy of community detection. The node labels after label propagation are calibrated according to the current attraction of the community to the nodes, which effectively improves the situation of misclassification in the early community detection. Finally, overlapping community detection is carried out based on the non-overlapping community structure. At this time, the overlapping community detection result is more accurate and interpretable. The community detection results on 3 synthetic networks and 12 real datasets show that the proposed algorithm has more advantages than four non-overlapping community detection methods and two overlapping community detection methods.

Detecting communities in complex networks using triangles and modularity density

The community structure is an important property of complex networks. Community detection of complex networks can be used to help reveal the relationship between topology and functionality. Modularity density QD, as a community quality function, has been widely used for detection of community structure in networks. Here, we develop a novel modularity density based on triangular motifs, and also prove its equivalence with the spectral clustering and non-negative matrix factorization. In addition, we develop a community detection method that incorporates the edge and triangular motif information, and apply the proposed method to several classical complex networks. Experiments show that the proposed method outperforms the standard modularity density QD.

Explore urban interactions based on floating car data – a case study of Chengdu, China

ABSTRACT Transport data are important for understanding human mobility and urban interactions within a city. As China’s transportation infrastructure continues to grow, more research is needed to analyse the spatial patterns of travel flows and to understand how these patterns change over time. With the development of online car-hailing and ride sharing services, floating car data have become a new resource to facilitate the analysis of human mobility patterns and the interactions of urban mobility within a city. The detection of urban communities based on urban networks is a helpful way to represent urban interactions. However, understanding community changes using online car-hailing data remains an underexplored topic. To this end, this study applies a community detection method to explore community changes over time based on the newly available floating car data (DiDi Chuxing (‘DiDi’)) in Chengdu, China. We applied undirected graphs to examine the spatial distribution of DiDi usage and the spatial patterns of travel distance. In addition, we explored the spatial-temporal variations of the communities at the taxi zone level using Blondel’s iterative algorithm, a modularity optimization approach. Results suggest that: 1) taxi zones on the south and west sides of Chengdu have more average daily trips compared to those in other areas; 2) residential taxi zones in the northeast area have a long median travel distance, indicating people living in those areas travel longer distances; and 3) the detected community structures change at different times. These findings provide valuable information for urban planning and location-based services in Chengdu.

Probabilistic Community Detection in Social Networks

The detection of community structures is a very crucial research area. The problem of community detection has received considerable attention from a large portion of the scientific community. More importantly, these articles are spread across a large number of different disciplines, from computer science, to statistics, and social sciences. The analysis of modern social networks becomes rather cumbersome, as their size and number keeps growing larger and larger. Moreover, in the modern communities, users participate in large number of groups. From the network perspective, efficient methods should be developed to automatically identify overlapping communities, that is, communities with overlapping nodes. In this work, we use a probabilistic network model to characterize and identify linked communities with common nodes. The innovative idea in this work is that the communities are represented as Markovian networks with continuously changing states. Each state represents the number of users within a cluster, that have specific characteristic classes. Based on the current state, we introduce a fast, linear on the number of newly added users, approach to estimate the probability of each cluster to be homogeneous in terms of sets of user characteristics and to determine how well the new user fit within a community. Because of the linear computations involved, our proposed probabilistic model can detect communities and overlaps with low execution time and high accuracy, as shown in our experimental results. The experimental results have shown that our probabilistic scheme executes faster and provides more robust communities compared to competitive schemes.

Important subgraph discovery using non-dominance criterion

Graph mining techniques have received a lot of attention to discover important subgraphs based on certain criteria. These techniques have become increasingly important due to the growing number of applications that rely on graph-based data. Some examples are: (i) microarray data analysis in bioinformatics, (ii) transportation network analysis, (iii) social network analysis. In this study, we propose a graph decomposition algorithm using the non-dominance criterion to identify important subgraphs based on two characteristics: edge connectivity and diameter. The proposed method uses a multi-objective optimization approach to maximize the edge connectivity and minimize the diameter. In a similar vein, identifying communities within a network can improve our comprehension of the network's characteristics and properties. Therefore, the detection of community structures in networks has been extensively studied. As a result, in this paper an innovative community detection method is presented based on our approach. The performance of the proposed technique is examined on both real-life and synthetically generated data sets.

A spectral method to detect community structure based on Coulomb’s matrix

A spectral method to detect community structure based on Coulomb’s matrix

Community structure detection in networks based on Tabu search

Community structure is a main structural feature of networks, which can model many complex systems. It illustrates a lot of information about networks like their internal organisation and the degree of similarity between network nodes. Many methods have been proposed to find community structure in networks. However, there is always requirement to new methods for many reasons especially the accuracy. In this paper, we present a new method to find community structure in networks. Our method is hierarchical algorithm based on Tabu Search metaheuristic. A dendrogram is built by our method after dividing a network several times. The community structure will be selected from the built dendrogram based on quality function called Modularity. Our method has been tested on artificial benchmark and real networks. Results demonstrate the superiority of our method compared with several state-of-art methods.