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.     

Semi-supervised clustering algorithm for community structure detection in complex networks

Discovering a community structure is fundamental for uncovering the links between structure and function in complex networks. In this paper, we discuss an equivalence of the objective functions of the symmetric nonnegative matrix factorization (SNMF) and the maximum optimization of modularity density. Based on this equivalence, we develop a new algorithm, named the so-called SNMF-SS, by combining SNMF and a semi-supervised clustering approach. Previous NMF-based algorithms often suffer from the restriction of measuring network topology from only one perspective, but our algorithm uses a semi-supervised mechanism to get rid of the restriction. The algorithm is illustrated and compared with spectral clustering and NMF by using artificial examples and other classic real world networks. Experimental results show the significance of the proposed approach, particularly, in the cases when community structure is obscure.     

Phase synchronization on small-world networks with community structure

In this paper, we propose a simple model that can generate small-world network with community structure. The network is introduced as a tunable community organization with parameter r, which is directly measured by the ratio of inter- to intra-community connectivity, and a smaller r corresponds to a stronger community structure. The structure properties, including the degree distribution, clustering, the communication efficiency and modularity are also analysed for the network. In addition, by using the Kuramoto model, we investigated the phase synchronization on this network, and found that increasing the fuzziness of community structure will markedly enhance the network synchronizability; however, in an abnormal region (r ≤ 0.001), the network has even worse synchronizability than the case of isolated communities (r = 0). Furthermore, this network exhibits a remarkable synchronization behaviour in topological scales: the oscillators of high densely interconnected communities synchronize more easily, and more rapidly than the whole network.     

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     

基于节点间依赖度的社团结构划分方法

本文提出了一种基于节点间依赖度的在复杂网络中划分社团结构的算法,定义了节点对其邻居的依赖度以及节点对社团的依赖度和条件依赖度.算法的基本要点是优先将最大依赖度不小于其他节点且有惟一依赖节点的节点划分到社团,并将对社团的依赖度或条件依赖度达到一定值的节点吸收进社团,直到所有节点都得到准确的社团划分.本算法在几个实际网络的测试上,都成功地划分出了满足条件的社团,并且对社团结构已知的网络的划分结果符合实际情况.     

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.     

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.     

基于簇相似度的网络社团结构探测算法

社团结构对复杂系统的结构特性和动力学特性有重要影响.提出了一个度量社团相似度的模型,称为簇相似度.该模型能够度量两个社团的相似度大小,为研究社团间的作用机制提供帮助.而且基于该模型,设计了一个社团划分算法.算法采用层次聚类的思想,每次合并两个相似度最大的社团,并通过一个评价函数选择最优社团划分.数值实验以及与CNM,GN,EigenMod等主流算法做比较,表明本算法的精度和效率都比较高,尤其对于边密度较高的网络,性能非常理想.     

网络的模块矩阵及其社团结构指标

探讨了复杂网络的模块矩阵的正(负)特征谱与网络的社团结构(反社团结构)的关系,给出了反映网络社团结构性质的相关定义.利用模块矩阵的多个特征值与特征向量,引入反映个体对所处社团的依附程度一种结构中心化指标.利用人工网络与实际网络数据,将这种指标与几种经典的中心化指标进行了比较.结果表明该指标具有较好的分辨率并与度指标具有一定程度的相关性.     

An extended improved global structure model for influential node identification in complex networks

Accurate identification of influential nodes facilitates the control of rumor propagation and interrupts the spread of computer viruses. Many classical approaches have been proposed by researchers regarding different aspects. To explore the impact of location information in depth, this paper proposes an improved global structure model to characterize the influence of nodes. The method considers both the node's self-information and the role of the location information of neighboring nodes. First, degree centrality of each node is calculated, and then degree value of each node is used to represent self-influence, and degree values of the neighbor layer nodes are divided by the power of the path length, which is path attenuation used to represent global influence. Finally, an extended improved global structure model that considers the nearest neighbor information after combining self-influence and global influence is proposed to identify influential nodes. In this paper, the propagation process of a real network is obtained by simulation with the SIR model, and the effectiveness of the proposed method is verified from two aspects of discrimination and accuracy. The experimental results show that the proposed method is more accurate in identifying influential nodes than other comparative methods with multiple networks.     

Generating weighted community networks based on local events

Many realistic networks have community structures, namely, a network consists of groups of nodes within which links are dense but among which links are sparse. This paper proposes a growing network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Also, it utilizes the preferential attachment for building connections determined by nodes' strengths, which evolves dynamically during the growth of the system. The resulting network reflects the intrinsic community structure with generalized power-law distributions of nodes' degrees and strengths.     

A dynamic epidemic control model on uncorrelated complex networks

In this paper, a dynamic epidemic control model on the uncorrelated complex networks is proposed. By means of theoretical analysis, we found that the new model has a similar epidemic threshold as that of the susceptible-infectedrecovered （SIR） model on the above networks, but it can reduce the prevalence of the infected individuals remarkably. This result may help us understand epidemic spreading phenomena on real networks and design appropriate strategies to control infections.     

虚拟社区网络的演化过程研究

模拟了虚拟社区网络的演化过程并研究其拓扑结构.发现虚拟社区网络在演化过程中,节点的加入、边的加入、网络中度分布、节点的度与其加入网络时间的关系、平均度随时间的变化等方面与传统的无标度网络有所不符.根据国内某论坛的实际网络数据统计与分析,提出了虚拟社区网络的演化机理——虚拟社区网络构造算法.仿真结果表明,模拟以互联网论坛为代表的虚拟社区网络时,该模型能够得到与真实网络相符的特性. 关键词： 复杂网络 虚拟社区 无标度网络     

Synchronization of coupled logistic maps on random community networks

The collective synchronization of a system of coupled logistic maps on random community networks is investigated. It is found that the synchronizability of the community network is affected by two factors when the size of the network and the number of connections are fixed. One is the number of communities denoted by the parameter rn, and the other is the ratio σ of the connection probability p of each pair of nodes within each community to the connection probability q of each pair of nodes among different communities. Theoretical analysis and numerical results indicate that larger rn and smaller σ are the key to the enhancement of network synchronizability. We also testify synchronous properties of the system by analysing the largest Lyapunov exponents of the system.     

Quantum inspired evolutionary algorithm for community detection in complex networks

Community structure is indispensable to discover the potential property of complex network systems. In this paper we propose two algorithms (QIEA-net and iQIEA-net) to discover communities in social networks by optimizing modularity. Unlike many existing methods, the proposed algorithms adopt quantum inspired evolutionary algorithm (QIEA) to optimize a population of solutions and do not need to give the number of community beforehand, which is determined by optimizing the value of modularity function and needs no human intervention. In order to accelerate the convergence speed, in iQIEA-net, we apply the result of classical partitioning algorithm as a guiding quantum individual, which can instruct other quantum individuals' evolution. We demonstrate the potential of two algorithms on five real social networks. The results of comparison with other community detection algorithms prove our approaches have very competitive performance.     

A uniform framework of projection and community detection for one-mode network in bipartite networks

Projection is a widely used method in bipartite networks. However, each projection has a specific application scenario and differs in the forms of mapping for bipartite networks. In this paper, inspired by the network-based information exchange dynamics, we propose a uniform framework of projection. Subsequently, an information exchange rate projection based on the nature of community structures of a network(named IERCP) is designed to detect community structures of bipartite networks. Results from the synthetic and real-world networks show that the IERCP algorithm has higher performance compared with the other projection methods. It suggests that the IERCP may extract more information hidden in bipartite networks and minimize information loss.     

一种新的网络传播中最有影响力的节点发现方法

在复杂网络的传播模型研究中, 如何发现最具影响力的传播节点在理论和现实应用中都有重大的意义. 目前的研究一般使用节点的度数、紧密度、介数和K-shell等中心化指标来评价影响力, 这种方法虽然简单, 但是由于它们仅利用了节点自身的内部属性, 因而在评价影响力时精确度并不高, 普遍性适用性较弱.为了解决这个问题, 本文提出了KSC (K-shell and community centrality)指标模型. 此模型不但考虑了节点的内部属性, 而且还综合考虑了节点的外部属性, 例如节点所属的社区等. 然后利用SIR (susceptible-infected-recovered)模型对传播过程进行仿真, 实验证明所提出的方法可以更好地发现最具有影响力的节点, 且可适用于各种复杂网络. 本文为这项具有挑战性研究提供了新的思想和方法. 关键词： 复杂网络 最具影响力的节点 社区划分 中性化测量     

Synchronization speed of identical oscillators on community networks

Synchronizability of complex oscillators networks has attracted much research interest in recent years. In contrast, in this paper we investigate numerically the synchronization speed, rather than the synchronizability or synchronization stability, of identical oscillators on complex networks with communities. A new weighted community network model is employed here, in which the community strength could be tunable by one parameter δ. The results showed that the synchronization speed of identical oscillators on community networks could reach a maximal value when δ is around 0.1. We argue that this is induced by the competition between the community partition and the scale-free property of the networks. Moreover, we have given the corresponding analysis through the second least eigenvalue λ₂ of the Laplacian matrix of the network which supports the previous result that the synchronization speed is determined by the value of λ₂.     

Ordered community structure in networks

Community structure in networks is often a consequence of homophily, or assortative mixing, based on some attribute of the vertices. For example, researchers may be grouped into communities corresponding to their research topic. This is possible if vertex attributes have unordered discrete values, but many networks exhibit assortative mixing by some ordered (discrete or continuous) attribute, such as age or geographical location. In such cases, the identification of discrete communities may be difficult or impossible. We consider how the notion of community structure can be generalized to networks that have assortative mixing by ordered attributes. We propose a method of generating synthetic networks with ordered communities and investigate the effect of ordered community structure on the spread of infectious diseases. We also show that current community detection algorithms fail to recover community structure in ordered networks, and evaluate an alternative method using a layout algorithm to recover the ordering.     

Community detection in signed networks based on discrete-time model

Community detection in signed networks has been studied widely in recent years. In this paper, a discrete difference equation is proposed to imitate the consistently changing phases of the nodes. During the interaction, each node will update its phase based on the difference equation. Each node has many different nodes connected with it, and these neighbors have different influences on it. The similarity between two nodes is applied to describe the influences between them. Nodes with high positive similarities will get together and nodes with negative similarities will be far away from each other.Communities are detected ultimately when the phases of the nodes are stable. Experiments on real world and synthetic signed networks show the efficiency of detection performance. Moreover, the presented method gains better detection performance than two existing good algorithms.