Efficient overlapping community detection in huge real-world networks

The detection of overlapping community structure in networks can give insight into the structures and functions of many complex systems. In this paper, we propose a simple but efficient overlapping community detection method for very large real-world networks. Taking a high-quality, non-overlapping partition generated by existing, efficient, non-overlapping community detection methods as input, our method identifies overlapping nodes between each pair of connected non-overlapping communities in turn. Through our analysis on modularity, we deduce that, to become an overlapping node without demolishing modularity, nodes should satisfy a specific condition presented in this paper. The proposed algorithm outputs high quality overlapping communities by efficiently identifying overlapping nodes that satisfy the above condition. Experiments on synthetic and real-world networks show that in most cases our method is better than other algorithms either in the quality of results or the computational performance. In some cases, our method is the only one that can produce overlapping communities in the very large real-world networks used in the experiments.     

Overlapping community detection using a generative model for networks

Detecting overlapping communities is a challenging task in analyzing networks, where nodes may belong to more than one community. Many present methods optimize quality functions to extract the communities from a network. In this paper, we present a probabilistic method for detecting overlapping communities using a generative model. The model describes the probability of generating a network with the model parameters, which reflect the communities in the network. The community memberships of each node are determined based on a probabilistic approach using those model parameters, whose values can be obtained by fitting the model to the network. This method has the advantage that the node participation degrees in each community are also computed. The proposed method is compared with some other community detection methods on both synthetic networks and real-world networks. The experiments show that this method is efficient at detecting overlapping communities and can provide better performance on the networks where a majority of nodes belong to more than one community.     

A fast and efficient heuristic algorithm for detecting community structures in complex networks

Community structure is an important property of complex networks. How to detect the communities is significant for understanding the network structure and to analyze the network properties. Many algorithms, such as K-L and GN, have been proposed to detect community structures in complex networks. According to daily experience, a community should have many nodes and connections. Based on these principles and existing researches, a fast and efficient algorithm for detecting community structures in complex networks is proposed in this paper. The key strategy of the algorithm is to mine a node with the closest relations with the community and assign it to this community. Four real-world networks are used to test the performance of the algorithm. Experimental results demonstrate that the algorithm proposed is rather efficient for detecting community structures in complex networks.     

A local fuzzy method based on “p-strong” community for detecting communities in networks

In this paper,we propose a local fuzzy method based on the idea of "p-strong" community to detect the disjoint and overlapping communities in networks.In the method,a refined agglomeration rule is designed for agglomerating nodes into local communities,and the overlapping nodes are detected based on the idea of making each community strong.We propose a contribution coefficient b_v~(ci)to measure the contribution of an overlapping node to each of its belonging communities,and the fuzzy coefficients of the overlapping node can be obtained by normalizing the b_v~(ci) to all its belonging communities.The running time of our method is analyzed and varies linearly with network size.We investigate our method on the computergenerated networks and real networks.The testing results indicate that the accuracy of our method in detecting disjoint communities is higher than those of the existing local methods and our method is efficient for detecting the overlapping nodes with fuzzy coefficients.Furthermore,the local optimizing scheme used in our method allows us to partly solve the resolution problem of the global modularity.     

Fuzzy overlapping community detection based on local random walk and multidimensional scaling

A fuzzy overlapping community is an important kind of overlapping community in which each node belongs to each community to different extents. It exists in many real networks but how to identify a fuzzy overlapping community is still a challenging task. In this work, the concept of local random walk and a new distance metric are introduced. Based on the new distance measurement, the dissimilarity index between each node of a network is calculated firstly. Then in order to keep the original node distance as much as possible, the network structure is mapped into low-dimensional space by the multidimensional scaling (MDS). Finally, the fuzzy c$c$-means clustering is employed to find fuzzy communities in a network. The experimental results show that the proposed algorithm is effective and efficient to identify the fuzzy overlapping communities in both artificial networks and real-world networks.     

Detecting community structure in complex networks based on a measure of information discrepancy

Properties of complex networks, such as small-world property, power-law degree distribution, network transitivity, and network- community structure which seem to be common to many real-world networks have attracted great interest among researchers. In this study, global information of the networks is considered by defining the profile of any node based on the shortest paths between it and all the other nodes in the network; then a useful iterative procedure for community detection based on a measure of information discrepancy and the popular modular function Q is presented. The new iterative method does not need any prior knowledge about the community structure and can detect an appropriate number of communities, which can be hub communities or non-hub communities. The computational results of the method on real networks confirm its capability.     

A thermal flux-diffusing model for complex networks and its applications in community structure detection

We introduce a thermal flux-diffusing model for complex networks. Based on this model, we propose a physical method to detect the communities in the complex networks. The method allows us to obtain the temperature distribution of nodes in time that scales linearly with the network size. Then, the local community enclosing a given node can be easily detected for the reason that the dense connections in the local communities lead to the temperatures of nodes in the same community being close to each other. The community structure of a network can be recursively detected by randomly choosing the nodes outside the detected local communities. In the experiments, we apply our method to a set of benchmarking networks with known pre-determined community structures. The experiment results show that our method has higher accuracy and precision than most existing globe methods and is better than the other existing local methods in the selection of the initial node. Finally, several real-world networks are investigated.     

Detecting overlapping communities of weighted networks via a local algorithm

Identification of communities is significant in understanding the structures and functions of networks. Since some nodes naturally belong to several communities, the study of overlapping communities has attracted increasing attention recently, and many algorithms have been designed to detect overlapping communities. In this paper, an overlapping communities detecting algorithm is proposed whose main strategies are finding an initial partial community from a node with maximal node strength and adding tight nodes to expand the partial community. Seven real-world complex networks and one synthetic network are used to evaluate the algorithm. Experimental results demonstrate that the algorithm proposed is efficient for detecting overlapping communities in weighted networks.     

Detecting local community structures in complex networks based on local degree central nodes

Detecting local communities in real-world graphs such as large social networks, web graphs, and biological networks has received a great deal of attention because obtaining complete information from a large network is still difficult and unrealistic nowadays. In this paper, we define the term local degree central node whose degree is greater than or equal to the degree of its neighbor nodes. A new method based on the local degree central node to detect the local community is proposed. In our method, the local community is not discovered from the given starting node, but from the local degree central node that is associated with the given starting node. Experiments show that the local central nodes are key nodes of communities in complex networks and the local communities detected by our method have high accuracy. Our algorithm can discover local communities accurately for more nodes and is an effective method to explore community structures of large networks.     

Recursive filtration method for detecting community structure in networks

Community detection is a topic of considerable recent interest within complex networks, but most methods proposed so far are divisive and agglomerative methods which delete only one edge each time to split the network, or agglomerating only one node each time until no individual node remains. Unlike those, we propose a method to split networks in parallel by deleting many edges in each filtration operation, and propose a community recursive coefficient (CRC) denoted by M instead of Q (modularity) to quantify the effect of the splitting results in this paper. We proved that recursive optimizing of the local M is equivalent to acquiring the maximal global Q value corresponding to good divisions. For a network with m edges, c communities and arbitrary topology, the method split the network at most c+1 times and detected the community structure in time O(m²+(c+1)m). We give several example applications, and show that the method can detect local communities according to the densities of external links to them in increasing order especially in large networks.     

A time-series approach to measuring node similarity in networks and its application to community detection

A central concept in network analysis is that of similarity between nodes. In this paper, we introduce a dynamic time-series approach to quantifying the similarity between nodes in networks. The problem of measuring node similarity is exquisitely embedded into the framework of time series for state evolution of nodes. We develop a deterministic parameter-free diffusion model to drive the dynamic evolution of node states, and produce a unique time series for each source node. Then we introduce a measure quantifying how far all the other nodes are located from each source one. Following this measure, a quantity called dissimilarity index is proposed to signify the extent of similarity between nodes. Thereof, our dissimilarity index gives a deep and natural integration between the local and global perspectives of topological structure of networks. Furthermore, we apply our dissimilarity index to unveil community structure in networks, which verifies the proposed dissimilarity index.     

Fuzzy analysis of community detection in complex networks

A snowball algorithm is proposed to find community structures in complex networks by introducing the definition of community core and some quantitative conditions. A community core is first constructed, and then its neighbors, satisfying the quantitative conditions, will be tied to this core until no node can be added. Subsequently, one by one, all communities in the network are obtained by repeating this process. The use of the local information in the proposed algorithm directly leads to the reduction of complexity. The algorithm runs in O(n+m) time for a general network and O(n) for a sparse network, where n is the number of vertices and m is the number of edges in a network. The algorithm fast produces the desired results when applied to search for communities in a benchmark and five classical real-world networks, which are widely used to test algorithms of community detection in the complex network. Furthermore, unlike existing methods, neither global modularity nor local modularity is utilized in the proposal. By converting the considered problem into a graph, the proposed algorithm can also be applied to solve other cluster problems in data mining.     

Ant colony clustering with fitness perception and pheromone diffusion for community detection in complex networks

Community structure detection in complex networks has been intensively investigated in recent years. In this paper, we propose an adaptive approach based on ant colony clustering to discover communities in a complex network. The focus of the method is the clustering process of an ant colony in a virtual grid, where each ant represents a node in the complex network. During the ant colony search, the method uses a new fitness function to percept local environment and employs a pheromone diffusion model as a global information feedback mechanism to realize information exchange among ants. A significant advantage of our method is that the locations in the grid environment and the connections of the complex network structure are simultaneously taken into account in ants moving. Experimental results on computer-generated and real-world networks show the capability of our method to successfully detect community structures.     

Fuzzy modularity and fuzzy community structure in networks

To find the fuzzy community structure in a complex network, in which each node has a certain probability of belonging to a certain community, is a hard problem and not yet satisfactorily solved over the past years. In this paper, an extension of modularity, the fuzzy modularity is proposed, which can provide a measure of goodness for the fuzzy community structure in networks. The simulated annealing strategy is used to maximize the fuzzy modularity function, associating with an alternating iteration based on our previous work. The proposed algorithm can efficiently identify the probabilities of each node belonging to different communities with random initial fuzzy partition during the cooling process. An appropriate number of communities can be automatically determined without any prior knowledge about the community structure. The computational results on several artificial and real-world networks confirm the capability of the algorithm.     

Overlapping Community Detection Based on Membership Degree Propagation

A community in a complex network refers to a group of nodes that are densely connected internally but with only sparse connections to the outside. Overlapping community structures are ubiquitous in real-world networks, where each node belongs to at least one community. Therefore, overlapping community detection is an important topic in complex network research. This paper proposes an overlapping community detection algorithm based on membership degree propagation that is driven by both global and local information of the node community. In the method, we introduce a concept of membership degree, which not only stores the label information, but also the degrees of the node belonging to the labels. Then the conventional label propagation process could be extended to membership degree propagation, with the results mapped directly to the overlapping community division. Therefore, it obtains the partition result and overlapping node identification simultaneously and greatly reduces the computational time. The proposed algorithm was applied to a synthetic Lancichinetti–Fortunato–Radicchi (LFR) dataset and nine real-world datasets and compared with other up-to-date algorithms. The experimental results show that our proposed algorithm is effective and outperforms the comparison methods on most datasets. Our proposed method significantly improved the accuracy and speed of the overlapping node prediction. It can also substantially alleviate the computational complexity of community structure detection in general.     

LPA-MNI: An Improved Label Propagation Algorithm Based on Modularity and Node Importance for Community Detection

Community detection is of great significance in understanding the structure of the network. Label propagation algorithm (LPA) is a classical and effective method, but it has the problems of randomness and instability. An improved label propagation algorithm named LPA-MNI is proposed in this study by combining the modularity function and node importance with the original LPA. LPA-MNI first identify the initial communities according to the value of modularity. Subsequently, the label propagation is used to cluster the remaining nodes that have not been assigned to initial communities. Meanwhile, node importance is used to improve the node order of label updating and the mechanism of label selecting when multiple labels are contained by the maximum number of nodes. Extensive experiments are performed on twelve real-world networks and eight groups of synthetic networks, and the results show that LPA-MNI has better accuracy, higher modularity, and more reasonable community numbers when compared with other six algorithms. In addition, LPA-MNI is shown to be more robust than the traditional LPA algorithm.     

Detecting overlapping communities in networks via dominant label propagation

Community detection is an important methodology for understanding the intrinsic structure and function of a realworld network.In this paper,we propose an effective and efficient algorithm,called Dominant Label Propagation Algorithm(Abbreviated as DLPA),to detect communities in complex networks.The algorithm simulates a special voting process to detect overlapping and non-overlapping community structure in complex networks simultaneously.Our algorithm is very efficient,since its computational complexity is almost linear to the number of edges in the network.Experimental results on both real-world and synthetic networks show that our algorithm also possesses high accuracies on detecting community structure in networks.     

加权网络权重自相似评判函数及其社团结构检测

提出了权重自相似性加权网络社团结构评判函数,并基于该函数提出一种谱分析算法检测社团结构,结果表明算法能将加权网络划分为同一社团内边权值分布均匀,而社团间边权值分布随机的社团结构.通过建立具有社团结构的加权随机网络分析了该算法的准确性,与WEO和WGN算法相比,在评判权重自相似的阈值系数取较小时,该算法具有较高的准确性.对于一个具有n个节点和c个社团的加权网络,社团结构检测的复杂度为O(cn2/2).通过设置评判权重自相似的阈值系数,可检测出能反映节点联系稳定性的层化性社团结构.这与传统意义上只将加权网络划分为社团中边权值较大而社团间边权值较小的标准不同,从另一个角度更好地提取了加权网络的结构信息.     

Community detection in complex networks by density-based clustering

We proposed a method to find the community structure in a complex network by density-based clustering. Physical topological distance is introduced in density-based clustering for determining a distance function of specific influence functions. According to the distribution of the data, the community structures are uncovered. The method keeps a better connection mode of the community structure than the existing algorithms in terms of modularity, which can be viewed as a basic characteristic of community detection in the future. Moreover, experimental results indicate that the proposed method is efficient and effective to be used for community detection of medium and large networks.     

复杂网络中社团结构发现的多分辨率密度模块度

现实中的许多复杂网络呈现出明显的模块性或社团性.模块度是衡量社团结构划分优劣的效益函数, 它也通常被用作社团结构探测的目标函数,但最为广泛使用的Newman-Girvan模块度却存在着分辨率限制问题,多分辨率模块度也不能克服误合并社团和误分裂社团同时存在的缺陷. 本文在网络密度的基础上提出了多分辨率的密度模块度函数, 通过实验和分析证实了该函数能够使社团结构的误划分率显著降低, 而且能够体现出网络社团结构是一个有机整体,不是各个社团的简单相加.