Community Structure In Complex Networks Research Articles

Exploring the Community Structure of Complex Networks

Regarding complex networks, one of the most relevant problems is to understand and to explore community structure. In particular it is important to define the network organization and the functions associated to the different network partitions. In this context, the idea is to consider some new approaches based on interval data in order to represent the different relevant network components as communities. The method is also useful to represent the network community structure, especially the network hierarchical structure. The application of the methodologies is based on the Italian interlocking directorship network.

Scalably revealing the dynamics of soft community structure in complex networks

Revealing the dynamics of community structure is of great concern for scientists from many fields. Specifically, how to quantify the dynamic details of soft community structure is a very interesting topic. In this paper, the authors propose a novel framework to study the scalable dynamic behavior of the soft community structure. First, the authors model the Potts dynamics to detect community structure using a “soft” Markov process. Then the soft stability of in a multiscale view is proposed to naturally uncover the local uniform behavior of spin values across multiple hierarchical levels. Finally, a new partition index is developed to detect fuzzy communities based on the stability and the dynamical information. Experiments on the both synthetically generated and real-world networks verify that the framework can be used to uncover hierarchical community structures effectively and efficiently.

A general method of community detection by identifying community centers with affinity propagation

Detection of community structures is beneficial to analyzing the structures and properties of networks. It is of theoretical interest and practical significance in modern science. So far, a large number of algorithms have been proposed to detect community structures in complex networks, but most of them are suitable for a specific network structure. In this paper, a novel method (called CDMIC) is proposed to detect the communities in un-weighted, weighted, un-directed, directed and signed networks by constructing a dissimilarity distance matrix of network and identifying community centers with maximizing modularity. For a given network, we first estimate the distance between all pairs of nodes for constructing the dissimilarity distance matrix of the network. Then, this distance matrix is input to the affinity propagation (AP) algorithm to extract a candidate center set of community. Thirdly, we rank these centers in descending order according to the sum of their availability and responsibility. Finally, we determine the community structure by selecting the center subset from the candidate center set in an incremental manner to make the modularity maximization. On three real-world networks and some synthetic networks, experimental results show that our CDMIC method has higher performance in terms of classification accuracy and normalized mutual information (NMI), and ability to tolerate the resolution limitation.

Hierarchical mutual information for the comparison of hierarchical community structures in complex networks.

The quest for a quantitative characterization of community and modular structure of complex networks produced a variety of methods and algorithms to classify different networks. However, it is not clear if such methods provide consistent, robust, and meaningful results when considering hierarchies as a whole. Part of the problem is the lack of a similarity measure for the comparison of hierarchical community structures. In this work we give a contribution by introducing the hierarchical mutual information, which is a generalization of the traditional mutual information and makes it possible to compare hierarchical partitions and hierarchical community structures. The normalized version of the hierarchical mutual information should behave analogously to the traditional normalized mutual information. Here the correct behavior of the hierarchical mutual information is corroborated on an extensive battery of numerical experiments. The experiments are performed on artificial hierarchies and on the hierarchical community structure of artificial and empirical networks. Furthermore, the experiments illustrate some of the practical applications of the hierarchical mutual information, namely the comparison of different community detection methods and the study of the consistency, robustness, and temporal evolution of the hierarchical modular structure of networks.

A new algorithm CNM-Centrality of detecting communities based on node centrality

The discovery and analysis of community structure in complex networks is a hot issue in recent years. In this paper, based on the fast greedy clustering algorithm CNM with the thought of local search, the introduction of the idea of node centrality and the optimal division of the central nodes and their neighbor nodes into correct communities, a new algorithm CNM-Centrality of detecting communities in complex networks is proposed. In order to verify the accuracy and efficiency of this algorithm, the performance of this algorithm is tested on several representative real-world networks and a set of computer-generated networks by LFR-benchmark. The experimental results indicate that this algorithm can identify the communities accurately and efficiently. Furthermore, this algorithm can also acquire higher values of modularity and NMI than the CNM, Infomap, Walktrap algorithms do.

The comparison of significance of fuzzy community partition across optimization methods

The analysis of fuzzy(overlapping) community structure in complex networks is an important problem in data mining of network data sets. However, due to the exist of random factors and error edges in real networks, how to measure the significance of community structure efficiently is a crucial question. In this paper, we present a novel statistical framework comparing the significance of fuzzy community structure across various optimization models. Different from the universal approaches, we calculate the similarity between a given node and its leader and employ the distribution of link tightness to derive the significance score, instead of a direct comparison to a randomized model. Based on the distribution of community tightness, a new p- value form significance measure is proposed for community structure analysis. Specially, the well-known approaches and their corresponding quality functions are unified to a novel general formulation, which facilitate providing a detail comparison across them. To determine the position of leaders and their corresponding followers, an efficient algorithm is proposed based on the spectral theory. Finally, we apply the significance analysis to some famous benchmark networks and the good performance verified the effectiveness and efficiency of our framework.

Topic-oriented community detection of rating-based social networks

Nowadays, real world social networks contain a vast range of information including shared objects, comments, following information, etc. Finding meaningful communities in this kind of networks is an interesting research area and has attracted the attention of many researchers. The community structure of complex networks reveals both their organization and hidden relations among their constituents. Most of the researches in the field of community detection mainly focus on the topological structure of the network without performing any content analysis. In recent years, a number of researches have proposed approaches which consider both the contents that are interchanged in networks, and the topological structures of the networks in order to find more meaningful communities. In this research, the effect of topic analysis in finding more meaningful communities in social networking sites in which the users express their feelings toward different objects (like movies) by means of rating is demonstrated by performing extensive experiments.

Community Detection Utilizing a Novel Multi-swarm Fruit Fly Optimization Algorithm with Hill-Climbing Strategy

The community detection methods based on evolutionary algorithm have become a hot research topic in recent years. However, most contemporary evolution-based community detection algorithms need many parameters in the initialization process and are characterized by complicated computational processes, which are puzzled for users to have a better understanding of these parameters on the performance of corresponding algorithm. In this paper, we first propose a new community detection method utilizing multi-swarm fruit fly optimization algorithm (CDMFOA), which needs only a few parameters and has a simple computational process. Moreover, we adopt the multi-swarm fruit fly strategy and hill-climbing method in community detection algorithm in order to resolve the premature convergence and improve the local search ability of CDMFOA. Meanwhile, we separately utilize modularity and modularity density as objective function in the framework of the CDMFOA, named CDMFOA_Q and CDMFOA_D, so as to check their detection abilities and accuracies in partitioning communities of complex networks. The experimental results on synthetic and real-world networks show that CDMFOA can effectively detect community structure in complex networks. Besides, we also demonstrate that the CDMFOA_D performs better than CDMFOA_Q and other traditional modularity-based methods.

Leaders in communities of real-world networks

Community structures have important influence on the properties and dynamic characteristics of the complex networks. However, to the best of our knowledge, there is not much attention given to investigating the internal structure of communities in the literature. In this paper, we study community structures of more than twenty existing networks using ten commonly used community-detecting methods, and discovery that most communities have several leaders whose degrees are particularly large. We use statistical parameter, variance, to classify the communities as leader communities and self-organized communities. In a leader community, we defined the nodes with largest 10% degree as its leaders. In our experiences, when removing the leaders, on average community’s internal edges are reduced by more than 40% and inter-communities edges are reduced by more than 20%. In addition, community’s average clustering coefficient decreases. These facts suggest that the leaders play an important role in keeping communities denser and more clustered, and it is the leaders that are more likely to link to other communities. Moreover, similar results for several random networks are obtained, and a theoretical lower bound of the lost internal edges is given. Our study shed the light on the further understanding and application of the internal community structure in complex networks.

Noisy extremal optimization

Noisy extremal optimization is a new optimization-based heuristic designed to identify the community structure of complex networks by maximizing the modularity function. The extremal optimization algorithm evolves configurations that represent network covers, composed of nodes evaluated separately. Each iteration, a number of nodes having the worst fitness values are randomly assigned different communities. A network shifting procedure is used to induce a noise in the population as a diversity preserving mechanism. Numerical experiments, performed on synthetic and real-world networks, illustrate the potential of this approach.

Overlapping community detection in complex networks using multi-objective evolutionary algorithm

Community structure is an important topological property of complex networks, which has great significance for understanding the function and organization of networks. Generally, community detection can be formulated as a single-objective or multi-objective optimization problem. Most existing optimization-based community detection algorithms are only applicable to disjoint community structure. However, it has been shown that in most real-world networks, a node may belong to multiple communities implying overlapping community structure. In this paper, we propose a multi-objective evolutionary algorithm for identifying overlapping community structure in complex networks based on the framework of non-dominated sorting genetic algorithm. Two negatively correlated evaluation metrics of community structure, termed as negative fitness sum and unfitness sum, are adopted as the optimization objectives. In our algorithm, link-based adjacency representation of overlapping community structure and a population initialization method based on local expansion are proposed. Extensive experimental results on both synthetic and real-world networks demonstrate that the proposed algorithm is effective and promising in detecting overlapping community structure in complex networks.

Identifying community structure in complex networks

A wide variety of applications could be formulated to resolve the problem of finding all communities from a given network, ranging from social and biological network analysis to web mining and searching. In this study, we propose the concept of virtual attractive strength between each pair of node in networks, and then give the definition of community structure based on the proposed attractive strength. Furthermore, we present a community detection method by moving vertices to the clusters that produce the largest attractive strengths to them until the division of network reaches unchanged. Experimental results on synthetic and real networks indicate that the proposed approach has favorite effectiveness and fast convergence speed, which provides an efficient method for exploring and analyzing complex systems.

Overlapping Community Detection by Local Community Expansion

Community structure is the key aspect of complex network analysis and it has important practical significance. While in real networks, some nodes may belong to multiple communities, so overlapping community detection attracts more and more attention. But most of the existing overlapping community detection algorithms increase the time complexity in some extent. In order to detect overlapping community structures in complex network more effectively, we propose a novel overlapping community detection method by local community expansion called OCDLCE. The proposed algorithm firstly partitions the network into small local communities using the local structural information, and then merges these communities to the final overlapping community structures. We present the concept of community connectivity as the criterion of community combination in the second stage of the proposed algorithm. The experimental results on both synthetic and real networks demonstrate that our algorithm improves the community detection performance, and at the same time, its time efficiency is better than the state-of-the-art methods.

Community detection based on local topological information and its application in power grid

Community structure detection algorithm is employed in a vast amount of study to partition a network into some loosely coupled sub-networks of smaller scale. It is an effective tool to analyze and control some large-scale networks such as power grids. This paper proposes a novel algorithm based on local similarity to detect the community structure in complex network. Firstly, a new similarity index between nodes is defined to model the topological closeness of local connections in networks. Then nodes sharing high similarity are gathered to form the community structure. The results suggest the emergence of the bridging nodes and kernels within the community detection process. This proposed method performs well when it is introduced to seek out the actual community structure, kernels and bridging nodes in some benchmark networks. Thirdly, the proposed algorithm lends itself to many applications, such as detecting communities in several IEEE standard power grids and investigating the roles of bridging nodes in cascading failures. Experimentally, the proposed algorithm outperforms some other similarity indices and clustering methods. Finally, a detailed comparison helps us get the conclusion that the traditional label propagation algorithm is a special case of the proposed algorithm.

A Method for Community Detection of Complex Networks Based on Hierarchical Clustering

Due to the development and popularization of Internet, there is more and more research focusing on complex networks. Research shows that there exists community structure in complex networks. Finding out community structure helps to extract useful information in complex networks, so the research on community detection is becoming a hotspot in recent years. There are two remarkable problems in detecting communities. Firstly, the detection accuracy is normally not very high; Secondly, the assessment criteria are not very effective when real communities are unknown. This paper proposes an algorithm for community detection based on hierarchical clustering (CDHC Algorithm). CDHC Algorithm firstly creates initial communities from global central nodes, then expands the initial communities layer by layer according to the link strength between nodes and communities, and at last merges some very small communities into large communities. This paper also proposes the concept of extensive modularity, overcoming some weakness of modularity. The extensive modularity can better evaluate the effectiveness of algorithms for community detection. This paper verifies the advantage of extensive modularity through experiments and compares CDHC Algorithm and some other representative algorithms for community detection on some frequently used datasets, so as to verify the effectiveness and advantages of CDHC Algorithm.

A novel cosine distance for detecting communities in complex networks

Detecting communities is significant to understand the potential structures and functions of complex systems. In order to detect communities more accurately and reasonably, a novel algorithm is proposed based on cosine distance and core-node in this paper. Cosine distances between nodes are regarded as their similarity measure and network node vectors can be extracted directly from the similarity matrix without calculating eigenvectors. Core-nodes as the initial communities are found by cosine distance threshold and degree threshold. Furthermore, the initial communities are expanded by adding other nodes with the nearest cosine distance to core-nodes. Through changing degree and cosine distance thresholds constantly, the optimal community structure of complex networks can be obtained by optimizing modularity with high accuracy. Experimental results on both real-world and synthetic networks demonstrate the feasibility and effectiveness of the proposed algorithm.

Community detection using local neighborhood in complex networks

It is common to characterize community structure in complex networks using local neighborhood. Existing related methods fail to estimate the accurate number of nodes present in each community in the network. In this paper a community detection algorithm using local community neighborhood ratio function is proposed. The proposed algorithm predicts vertex association to a specific community using visited node overlapped neighbors. In the beginning, the algorithm detects local communities; then through iterations and local neighborhood ratio function, final communities are detected by merging close related local communities. Analysis of simulation results on real and artificial networks shows the proposed algorithm detects well defined communities in both networks by wide margin.

Overlapping community detection through an improved multi-objective quantum-behaved particle swarm optimization

Community detection is one of the most important problems in the field of complex networks in recent years. The majority of present algorithms only find disjoint communities, however, community often overlap to some extent in many real-world networks. In this paper, an improved multi-objective quantum-behaved particle swarm optimization (IMOQPSO) based on spectral-clustering is proposed to detect the overlapping community structure in complex networks. Firstly, the line graph of the graph modeling the network is formed, and a spectral method is employed to extract the spectral information of the line graph. Secondly, IMOQPSO is employed to solve the multi-objective optimization problem so as to resolve the separated community structure in the line graph which corresponding to the overlapping community structure in the graph presenting the network. Finally, a fine-tuning strategy is adopted to improve the accuracy of community detection. The experiments on both synthetic and real-world networks demonstrate our method achieves cover results which fit the real situation in an even better fashion.

Analysis of community-detection methods based on Potts spin model in complex networks

Detection of community structures in complex networks is a common challenge in the study of complex networks. Recently, various methods have been proposed to discover community structures at different scales. Here, the multiscale methods based on Potts spin model for community detection are described and compared in the analysis of community structures of several networks. We give a critical analysis of the multiscale methods, showing a kind of limitation that the methods may suffer from when the community size difference is very broad, the breakup of (large) communities will appear before the merger of (small) communities disappears. In particular, we give the explicit expressions for the critical points of the merger and breakup of communities and derive the sufficient conditions (in the form of upper limits) that indicate when the Potts model methods suffer from the limitation. We apply the theoretical results to model networks and show that the method using the configuration null model (i.e., a random graph model as comparison that has the same degree distribution as the network under study) may not recover the full structure of the model network, whereas the method using the Erdös-Rényi null model will do so.

Detecting Multi-Scale Community Structure in Complex Networks

Multiple-scale community of complex networks has attracted much attention. For the problem, previous methods can not investigate multiple-scale property of community. To address this, we propose a novel algorithm (h_LPA) to detect multiple-scale structure of community. The algorithm is a heuristic label propagation algorithm associated with spectral analysis of complex networks. Label updating strategy of h_LPA is combined with heuristic function from the perspective of networks dynamics. The heuristic function further improves the dynamic efficiency of h_LPA. Extensive tests on artificial networks and real world networks give excellent results.