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.     

Research on Community Structure in Bus Transport Networks

We abstract the bus transport networks (BTNs) to two kinds of complex networks with space L and space P methods respectively. Using improved community detecting algorithm (PKM agglomerative algorithm), we analyze the community property of two kinds of BTNs graphs. The results show that the BTNs graph described with space L method have obvious community property, but the other kind of BTNs graph described with space P method have not. The reason is that the BTNs graph described with space P method have the intense overlapping community property and general community division algorithms can not identify this kind of community structure. To overcome this problem, we propose a novel community structure called N-depth community and present a corresponding community detecting algorithm, which can detect overlapping community. Applying the novel community structure and detecting algorithm to a BTN evolution model described with space P, whose network property agrees well with real BTNs', we get obvious community property.     

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.     

Detect overlapping and hierarchical community structure in networks

Clustering and community structure is crucial for many network systems and the related dynamic processes. It has been shown that communities are usually overlapping and hierarchical. However, previous methods investigate these two properties of community structure separately. This paper proposes an algorithm (EAGLE) to detect both the overlapping and hierarchical properties of complex community structure together. This algorithm deals with the set of maximal cliques and adopts an agglomerative framework. The quality function of modularity is extended to evaluate the goodness of a cover. The examples of application to real world networks give excellent results.     

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.     

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.     

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.     

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.     

Research on Community Structure in Bus Transport Networks

We abstract the bus transport networks （BTNs） to two kinds of complex networks with space L and space P methods respectively. Using improved community detecting algorithm （PKM agglomerative algorithm）, we analyze the community property of two kinds of BTNs graphs. The results show that the BTNs graph described with space L method have obvious community property, but the other kind of BTNs graph described with space P method have not. The reason is that the BTNs graph described with space P method have the intense overlapping community property and general community division algorithms can not identify this kind of community structure. To overcome this problem, we propose a novel community structure called N-depth community and present a corresponding community detecting algorithm, which can detect overlapping community. Applying the novel community structure and detecting algorithm to a BTN evolution model described with space P, whose network property agrees well with real BTNs＇, we get obvious community property.     

A game theoretic algorithm to detect overlapping community structure in networks

Community detection can be used as an important technique for product and personalized service recommendation. A game theory based approach to detect overlapping community structure is introduced in this paper. The process of the community formation is converted into a game, when all agents (nodes) cannot improve their own utility, the game process will be terminated. The utility function is composed of a gain and a loss function and we present a new gain function in this paper. In addition, different from choosing action randomly among join, quit and switch for each agent to get new label, two new strategies for each agent to update its label are designed during the game, and the strategies are also evaluated and compared for each agent in order to find its best result. The overlapping community structure is naturally presented when the stop criterion is satisfied. The experimental results demonstrate that the proposed algorithm outperforms other similar algorithms for detecting overlapping communities in networks.     

Synchronization on overlapping community network

In this paper, we propose a simple random network model with overlapping communities controlled by several parameters, and investigate the influence of the overlapping community structure on the synchronization behavior under different parameters. It is found that the synchronizability of the network is mainly influenced by the overlapping size of the communities and the connectivity density of the overlapped group to the other interrelated communities, and has nothing to do with the intra-connectivity of the overlapped group. In addition, it is found that the highly interconnected communities can be almost synchronized in a given time scale, whereas the overlapped group is far from synchronization. Furthermore, the instantaneous frequencies of the nodes in the communities and their overlapped group are also investigated, which show that the nodes in the overlapped group will exhibit a remarkable oscillation with a weighted mean frequency of the other correlative communities.     

Detecting overlapping communities based on vital nodes in complex networks

Detection of community structures in the complex networks is significant to understand the network structures and analyze the network properties. However, it is still a problem on how to select initial seeds as well as to determine the number of communities. In this paper, we proposed the detecting overlapping communities based on vital nodes algorithm(DOCBVA), an algorithm based on vital nodes and initial seeds to detect overlapping communities. First, through some screening method, we find the vital nodes and then the seed communities through the pretreatment of vital nodes. This process differs from most existing methods, and the speed is faster. Then the seeds will be extended. We also adopt a new parameter of attribution degree to extend the seeds and find the overlapping communities. Finally, the remaining nodes that have not been processed in the first two steps will be reprocessed. The number of communities is likely to change until the end of algorithm. The experimental results using some real-world network data and artificial network data are satisfactory and can prove the superiority of the DOCBVA algorithm.     

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.     

Detecting community structure in complex networks via node similarity

The detection of the community structure in networks is beneficial to understand the network structure and to analyze the network properties. Based on node similarity, a fast and efficient method for detecting community structure is proposed, which discovers the community structure by iteratively incorporating the community containing a node with the communities that contain the nodes with maximum similarity to this node to form a new community. The presented method has low computational complexity because of requiring only the local information of the network, and it does not need any prior knowledge about the communities and its detection results are robust on the selection of the initial node. Some real-world and computer-generated networks are used to evaluate the performance of the presented method. The simulation results demonstrate that this method is efficient to detect community structure in complex networks, and the ZLZ metrics used in the proposed method is the most suitable one among local indices in community detection.     

Community structure discovery method based on the Gaussian kernel similarity matrix

Community structure discovery in complex networks is a popular issue, and overlapping community structure discovery in academic research has become one of the hot spots. Based on the Gaussian kernel similarity matrix and spectral bisection, this paper proposes a new community structure discovery method. First, by adjusting the Gaussian kernel parameter to change the scale of similarity, we can find the corresponding non-overlapping community structure when the value of the modularity is the largest relatively. Second, the changes of the Gaussian kernel parameter would lead to the unstable nodes jumping off, so with a slight change in method of non-overlapping community discovery, we can find the overlapping community nodes. Finally, synthetic data, karate club and political books datasets are used to test the proposed method, comparing with some other community discovery methods, to demonstrate the feasibility and effectiveness of this method.     

Detecting overlapping communities by seed community in weighted complex networks

Detection of community structures in the weighted complex networks is significant to understand the network structures and analysis of the network properties. We present a unique algorithm to detect overlapping communities in the weighted complex networks with considerable accuracy. For a given weighted network, all the seed communities are first extracted. Then to each seed community, more community members are absorbed using the absorbing degree function. In addition, our algorithm successfully finds common nodes between communities. The experiments using some real-world networks show that the performance of our algorithm is satisfactory.     

基于社团结构的城市地铁网络模型研究

本文运用复杂网络理论, 对我国北京、上海、广州和深圳等城市的地铁网络进行了实证研究. 分别研究了地铁网络的度分布、聚类系数和平均路径长度. 研究表明, 该网络具有高的聚类系数和短的平均路径长度, 显示小世界网络的特征, 其度分布并不严格服从幂律分布或指数分布, 而是呈多段的分布, 显示层次网络的特征. 此外, 它还具有重叠的社团结构特征. 基于实证研究的结果, 提出一种基于社团结构的交通网络模型, 并对该模型进行了模拟分析, 模拟结果表明, 该模型的模拟结果与实证研究结果相符. 此外, 该模型还能解释其他类型的复杂网络(如城市公共汽车交通网络)的网络特性. 关键词： 复杂网络 地铁网络 小世界 社团     

Modelling of weighted evolving networks with community structures

Many social and biological networks consist of communities–groups of nodes within which links are dense but among which links are sparse. It turns out that most of these networks are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the link weights among their nodes. Recently, there are considerable interests in the study of properties as well as modelling of such networks with community structures. To our knowledge, however, no study of any weighted network model with such a community structure has been presented in the literature to date. In this paper, we propose a weighted evolving network model with a community structure. The new network model is based on the inner-community and inter-community preferential attachments and preferential strengthening mechanism. Simulation results indicate that this network model indeed reflect the intrinsic community structure, with various power-law distributions of the node degrees, link weights, and node strengths.     

Overlapping Community Detection Based on Attribute Augmented Graph

There is a wealth of information in real-world social networks. In addition to the topology information, the vertices or edges of a social network often have attributes, with many of the overlapping vertices belonging to several communities simultaneously. It is challenging to fully utilize the additional attribute information to detect overlapping communities. In this paper, we first propose an overlapping community detection algorithm based on an augmented attribute graph. An improved weight adjustment strategy for attributes is embedded in the algorithm to help detect overlapping communities more accurately. Second, we enhance the algorithm to automatically determine the number of communities by a node-density-based fuzzy k-medoids process. Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed algorithms can effectively detect overlapping communities with fewer parameters compared to the baseline methods.     

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.