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.     

Studies on controllability of directed networks with extremal optimization

Almost all natural, social and man-made-engineered systems can be represented by a complex network to describe their dynamic behaviors. To make a real-world complex network controllable with its desired topology, the study on network controllability has been one of the most critical and attractive subjects for both network and control communities. In this paper, based on a given directed–weighted network with both state and control nodes, a novel optimization tool with extremal dynamics to generate an optimal network topology with minimum control nodes and complete controllability under Kalman’s rank condition has been developed. The experimental results on a number of popular benchmark networks show the proposed tool is effective to identify the minimum control nodes which are sufficient to guide the whole network’s dynamics and provide the evolution of network topology during the optimization process. We also find the conclusion: “the sparse networks need more control nodes than the dense, and the homogeneous networks need fewer control nodes compared to the heterogeneous” (Liu et al., 2011  [18]), is also applicable to network complete controllability. These findings help us to understand the network dynamics and make a real-world network under the desired control. Moreover, compared with the relevant research results on structural controllability with minimum driver nodes, the proposed solution methodology may also be applied to other constrained network optimization problems beyond complete controllability with minimum control nodes.     

Detecting communities by the core-vertex and intimate degree in complex networks

In this paper, we present a new approach to extract communities in the complex networks with considerable accuracy. We introduce the core-vertex and the intimate degree between the community and its neighboring vertices. First, we find the core-vertices as the initial community. These core-vertices are then expanded using intimate degree function during extracting community structure from the given network. In addition, our algorithm successfully finds common nodes between communities. Experimental results using some real-world networks data shows that the performance of our algorithm is satisfactory.     

Density-based shrinkage for revealing hierarchical and overlapping community structure in networks

The investigation of community structure in networks is an important issue in many disciplines, which still remains a challenging task. First, complex networks often show a hierarchical structure with communities embedded within other communities. Moreover, communities in the network may overlap and have noise, e.g., some nodes belonging to multiple communities and some nodes marginally connected with the communities, which are called hub and outlier, respectively. Therefore, a good algorithm is desirable to be able to not only detect hierarchical communities, but also to identify hubs and outliers. In this paper, we propose a parameter-free hierarchical network clustering algorithm DenShrink. By combining the advantages of density-based clustering and modularity optimization methods, our algorithm can reveal the embedded hierarchical community structure efficiently in large-scale weighted undirected networks, and identify hubs and outliers as well. Moreover, it overcomes the resolution limit possessed by other modularity-based methods. Our experiments on the real-world and synthetic datasets show that DenShrink generates more accurate results than the baseline methods.     

Adjusting from disjoint to overlapping community detection of complex networks

The investigation of community structures is one of the most important problems in the field of complex networks and has countless applications in different disciplines: biology, computer, social sciences, etc. Many community detection algorithms have been developed in various fields recently. The vast majority of these algorithms only find disjoint communities; however, in many real-world networks communities often overlap to some extent. In this paper, we propose an efficient method for adjusting these classical algorithms to match the requirement for discovering overlapping communities in complex networks, which is based on a local definition of community strength. The method can in principle be applied with any clustering algorithm. Tests on a set of computer generated and real-world networks give excellent results. In particular, we show that the method can also allow one to availably analyze the problem of unstable nodes in community detection, which is very helpful for understanding the structural properties of the networks correctly and comprehensively.     

Community detection with consideration of non-topological information

In a network described by a graph, only topological structure information is considered to determine how the nodes are connected by edges. Non-topological information denotes that which cannot be determined directly from topological information. This paper shows, by a simple example where scientists in three research groups and one external group form four communities, that in some real world networks non-topological information (in this example, the research group affiliation) dominates community division. If the information has some influence on the network topological structure, the question arises as to how to find a suitable algorithm to identify the communities based only on the network topology. We show that weighted Newman algorithm may be the best choice for this example. We believe that this idea is general for real-world complex networks.     

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 Communities by Revised Max-flow Method in Networks

A ubiquitous phenomenon in networks is the presence of communities within which the network connections are dense and between which they are sparser.This paper proposes a max-flow algorithm in bipartite networks to detect communities in general networks.Firstly,we construct a bipartite network in accordance with a general network and derive a revised max-flow problem in order to uncover the community structure.Then we present a local heuristic algorithm to find the optimal solution of the revised max-flow problem.This method is applied to a variety of real-world and artificial complex networks,and the partition results confirm its effectiveness and accuracy.     

Detecting Communities by Revised Max-flow Method in Networks

A ubiquitous phenomenon in networks is the presence of communities within which the network connections are dense and between which they are sparser. This paper proposes a max-flow algorithm in bipartite networks to detect communities in general networks. Firstly, we construct a bipartite network in accordance with a general network and derive a revised max-flow problem in order to uncover the community structure. Then we present a local heuristic algorithm to find the optimal solution of the revised max-flow problem. This method is applied to a variety of real-world and artificial complex networks, and the partition results confirm its effectiveness and accuracy.     

复杂网络牵制控制优化选点算法及节点组重要性排序

本文研究复杂网络动力学模型的无向网络牵制控制的优化选点及节点组重要性排序问题.根据牵制控制的同步准则,网络的牵制控制同步取决于网络的Laplacian删后矩阵的最小特征值.因此,通过合理选择受控节点集得到一个较大的Laplacian删后矩阵最小特征值,是牵制控制优化选点问题的核心所在.基于Laplacian删后矩阵最小特征值的图谱性质,本文提出了多个受控节点选取的递归迭代算法,该算法适用于任意类型的网络.通过BA无标度网络、NW小世界网络及一些实际网络中的仿真实验表明:该算法在控制节点数较少时,能有效找到最优受控节点集.最后讨论了在复杂网络牵制控制背景下节点组重要性排序问题,提出节点组的重要性排序与受控节点的数目有关.     

Error and attack tolerance of synchronization in Hindmarsh–Rose neural networks with community structure

Synchronization is one of the most important features observed in large-scale complex networks of interacting dynamical systems. As is well known, there is a close relation between the network topology and the network synchronizability. Using the coupled Hindmarsh–Rose neurons with community structure as a model network, in this paper we explore how failures of the nodes due to random errors or intentional attacks affect the synchronizability of community networks. The intentional attacks are realized by removing a fraction of the nodes with high values in some centrality measure such as the centralities of degree, eigenvector, betweenness and closeness. According to the master stability function method, we employ the algebraic connectivity of the considered community network as an indicator to examine the network synchronizability. Numerical evidences show that the node failure strategy based on the betweenness centrality has the most influence on the synchronizability of community networks. With this node failure strategy for a given network with a fixed number of communities, we find that the larger the degree of communities, the worse the network synchronizability; however, for a given network with a fixed degree of communities, we observe that the more the number of communities, the better the network synchronizability.     

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.     

Evaluation of network robustness using a node tearing algorithm

Until recently the study of failure and vulnerability in complex networks focused on the role of high degree nodes, and the relationship between their removal and network connectivity. Recent evidence suggested that in some network configurations, the removal of lower degree nodes can also cause network fragmentation. We present a disassembling algorithm that identifies nodes that are core to network connectivity. The algorithm is based on network tearing in which communities are defined and used to construct a hierarchical structure. Cut-nodes, which are located at the boundaries of the communities, are the key interest. Their importance in the overall network connectivity is characterized by their participation with neighbouring communities in each level of the hierarchy. We examine the impact of these cut-nodes by studying the change in size of the giant component, local and global efficiencies, and how the algorithm can be combined with other community detection methods to reveal the finer internal structure within a community.     

确定度分布条件下可变同配系数的算法构造与影响分析

复杂网络是现实中大量节点和边的抽象拓扑, 如何揭示网络内部拓扑对网络连通性、脆弱性等特征的影响是当前研究的热点. 本文在确定度分布的条件下, 根据Newman提出的同配系数的定义分析其影响因素. 首先在可变同配系数下分别提出了基于度分布的确定算法和基于概率分布的不确定算法, 并分别在三种不同类型的网络(Erdös-Rényi网络, Barabási-Albert网络, Email真实网络)中验证. 实验结果表明: 当网络规模达到一定程度时, 确定算法优于贪婪算法. 以此为基础, 分析了同配系数改变时聚类系数的变化, 发现两者之间存在关联性, 并从网络的微观结构变化中揭示了聚类系数变化的原因.     

两相流流型复杂网络社团结构及其统计特性

利用气液两相流电导波动信号构建了流型复杂网络. 基于K均值聚类的社团探寻算法对该网络的社团结构进行了分析,发现该网络存在分别对应于泡状流、段塞流及混状流的三个社团,并且两个社团间联系紧密的点分别对应于相应的过渡流型. 基于复杂网络理论从全新的角度探讨了两相流流型复杂网络社团结构及统计特性问题,并取得了满意的流型识别效果,与此同时,在对该网络特性进一步分析的基础上,发现了对两相流流动参数变化敏感的相关复杂网络统计量,为更好地理解两相流流型动力学特性提供了参考. 关键词： 两相流流型 复杂网络 社团探寻算法 网络统计特性     

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.     

基于相对距离的复杂网络谱粗粒化方法

复杂网络的同步作为一种重要的网络动态特性,在通信、控制、生物等领域起着重要的作用.谱粗粒化方法是一种在保持原始网络的同步能力尽量不变情况下将大规模网络约简为小规模网络的算法.此方法在对约简节点分类时是以每个节点对应特征向量分量间的绝对距离作为判断标准,在实际运算中计算量大,可执行性较差.本文提出了一种以特征向量分量间相对距离作为分类标准的谱粗粒化改进算法,能够使节点的合并更加合理,从而更好地保持原始网络的同步能力.通过经典的三种网络模型(BA无标度网络、ER随机网络、NW小世界网络)和27种不同类型实际网络的数值仿真分析表明,本文提出的算法对比原来的算法能够明显改善网络的粗粒化效果,并发现互联网、生物、社交、合作等具有明显聚类结构的网络在采用谱粗粒化算法约简后保持同步的能力要优于电力、化学等模糊聚类结构的网络.     

Community detection based on network communicability

We propose a new method for detecting communities based on the concept of communicability between nodes in a complex network. This method, designated as N-ComBa K-means, uses a normalized version of the adjacency matrix to build the communicability matrix and then applies K-means clustering to find the communities in a graph. We analyze how this method performs for some pathological cases found in the analysis of the detection limit of communities and propose some possible solutions on the basis of the analysis of the ratio of local to global densities in graphs. We use four different quality criteria for detecting the best clustering and compare the new approach with the Girvan-Newman algorithm for the analysis of two "classical" networks: karate club and bottlenose dolphins. Finally, we analyze the more challenging case of homogeneous networks with community structure, for which the Girvan-Newman completely fails in detecting any clustering. The N-ComBa K-means approach performs very well in these situations and we applied it to detect the community structure in an international trade network of miscellaneous manufactures of metal having these characteristics. Some final remarks about the general philosophy of community detection are also discussed.     

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.