Detecting the structure of complex networks by quantum bosonic dynamics

In this paper, we introduce a non-interacting boson model to investigate the topological structure of complex networks. By exactly solving this model, we show that it provides a powerful analytical tool in uncovering the important properties of realistic networks. We find that the ground-state degeneracy of this model is equal to the number of connected components in a network and the square of each coefficient in the expansion of the ground state gives the average time that a random walker spends at each node in the infinite time limit. To show the usefulness of this approach in practice, we also carry out numerical simulations on some concrete complex networks. Our results are completely consistent with the previous conclusions derived by graph theory methods. Furthermore, we show that the first excited state appears always on the largest connected component of the network. The relationship between the first excited energy and the average shortest path length in networks is also discussed.     

Maximum entropy networks are more controllable than preferential attachment networks

A maximum entropy (ME) method to generate typical scale-free networks has been recently introduced. We investigate the controllability of ME networks and Barabási–Albert preferential attachment networks. Our experimental results show that ME networks are significantly more easily controlled than BA networks of the same size and the same degree distribution. Moreover, the control profiles are used to provide insight into control properties of both classes of network. We identify and classify the driver nodes and analyze the connectivity of their neighbors. We find that driver nodes in ME networks have fewer mutual neighbors and that their neighbors have lower average degree. We conclude that the properties of the neighbors of driver node sensitively affect the network controllability. Hence, subtle and important structural differences exist between BA networks and typical scale-free networks of the same degree distribution.     

Detecting the community structure in complex networks based on quantum mechanics

In this paper, we develop a novel method to detect the community structure in complex networks. This approach is based on the combination of kernel-based clustering using quantum mechanics, the spectral clustering technique and the concept of the Bayesian information criterion. We test the proposed algorithm on Zachary’s karate club network and the world of American college football. Experimental results indicate that our algorithm is efficient and effective at finding both the optimal number of clusters, and the best clustering of community structures.     

基于K-阶结构熵的网络异构性研究

结构熵可以考察复杂网络的异构性.为了弥补传统结构熵在综合刻画网络全局以及局部特性能力上的不足,本文依据网络节点在K步内可达的节点总数定义了K-阶结构熵,可从结构熵随K值的变化规律、最大K值下的结构熵以及网络能够达到的最小结构熵三个方面来评价网络的异构性.利用K-阶结构熵对规则网络、随机网络、Watts-Strogatz小世界网络、Barabási_-Albert无标度网络以及星型网络进行了理论研究与仿真实验,结果表明上述网络的异构性依次增强.其中K-阶结构熵能够较好地依据小世界属性来刻画小世界网络的异构性,且对星型网络异构性随其规模演化规律的解释也更为合理.此外, K-阶结构熵认为在规则结构外新增孤立节点的网络的异构性弱于未添加孤立节点的规则结构,但强于同节点数的规则网络.本文利用美国西部电网进一步论证了K-阶结构熵的有效性.     

Robustness measurement of scale-free networks based on motif entropy

As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structural integrity, functional integrity and dynamics of the networks. In order to overcome the shortcomings in the existing work on the robustness of complex networks, only nodes or edges are considered, while the defects of high-order structure in the network are ignored. From the perspective of network motif, we propose an entropy of node degree distribution based on motif to measure the robustness of scale-free networks under random attacks. The effectiveness and superiority of our method are verified and analyzed in the BA scale-free 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.     

一种基于最大流的网络结构熵

熵是可用来反映网络结构异质性的指标.针对传统熵指标不能很好反映网络全局异构性的不足,本文引入网络流的概念,综合考虑径向测度和中间测度,提出一种新的网络结构熵.特殊网络(如公用数据集Dolphins网络)的分析结果表明,本文提出的熵指标在一定程度上克服了其他网络熵指标的不足,更能够反映网络的真实拓扑结构;对随机网络、最近邻耦合网络、星型网络、无标度网络、Benchmark网络和小世界网络等典型网络的理论分析和仿真实验,进一步证明本文提出的熵指标在刻画一般复杂网络结构特征上的有效性和适用性.     

一种基于点和边差异性的网络结构熵

熵是反映网络异构性的重要指标. 由于只是关注网络结构中"点"或"边"的单一作用,基于度分布和度相对值的两种传统熵在刻画网络结构特征时均存在缺陷. 文章综合考虑"点"和"边"差异性,定义一种新的网络结构熵,并对规则网络、随机网络和无标度网络等结构熵进行理论分析和仿真实验. 结果表明,这种新网络结构熵可以更有效地反映网络的结构特征,尤其是对于稀疏网络及星型网络的结构差异解释更为合理. 关键词： 均匀网络 无标度网络 熵     

Efficient packet routing strategy in complex networks

We investigate a new efficient packet routing strategy which mitigates traffic congestion on complex networks. In order to avoid congestion, we minimize the maximum betweenness, which is a measure for concentration of routing paths passing through a node in the network. Danila et al. propose a packet routing strategy in which, instead of shortest paths, they used efficient paths, which are the paths with the minimum total summations of weights assigned to nodes in the respective paths. They use a heuristic algorithm in which the weights are updated step by step by using the information of betweenness of each node in every step and the respective total summations of weights for paths through the nodes with large degrees become comparatively large. Thus passage through such nodes, where congestion almost occurs, is likely to be avoided in their algorithm. The convergence time by their algorithm is, however, quite long. In this paper, we propose a new efficient heuristic algorithm which balances traffic on networks by achieving minimization of the maximum betweenness in the much smaller number of iteration steps for convergence than that by the algorithm of Danila et al.     

Epidemic spreading on weighted complex networks

Nowadays, the emergence of online services provides various multi-relation information to support the comprehensive understanding of the epidemic spreading process. In this Letter, we consider the edge weights to represent such multi-role relations. In addition, we perform detailed analysis of two representative metrics, outbreak threshold and epidemic prevalence, on SIS and SIR models. Both theoretical and simulation results find good agreements with each other. Furthermore, experiments show that, on fully mixed networks, the weight distribution on edges would not affect the epidemic results once the average weight of whole network is fixed. This work may shed some light on the in-depth understanding of epidemic spreading on multi-relation and weighted networks.     

Evolutionary minority game on complex networks

In this work we investigate the dynamics of networked evolutionary minority game (NEMG) wherein each agent is allowed to evolve its strategy according to the information obtained from its neighbors in the network. We investigate four kinds of networks, including star network, regular network, random network and scale-free network. Simulation results indicate that the dynamics of the system depends crucially on the structure of the underlying network. The strategy distribution in a star network is sensitive to the precise value of the mutation magnitude L, in contrast to the strategy distribution in regular, random and scale-free networks, which is easily affected by the value of the prize-to-fine ratio R. Under a simple evolutionary scheme, the networked system with suitable parameters evolves to a high level of global coordination among its agents. In particular, the performance of the system is correlated to the clustering property of the network, where larger clustering coefficient leads to better performance.     

Topology identification of weighted complex dynamical networks

Recently, various papers investigated the geometry features, synchronization and control of complex network provided with certain topology. While, the exact topology of a network is sometimes unknown or uncertain. Using Lyapunov theory, we propose an adaptive feedback controlling method to identify the exact topology of a rather general weighted complex dynamical network model. By receiving the network nodes evolution, the topology of such kind of network with identical or different nodes, or even with switching topology can be monitored. Experiments show that the methods presented in this paper are of high accuracy with good performance.     

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.     

Most probable degree distribution at fixed structural entropy

The structural entropy is the entropy of the ensemble of uncorrelated networks with given degree sequence. Here we derive the most probable degree distribution emerging when we distribute stubs (or half-edges) randomly through the nodes of the network by keeping fixed the structural entropy. This degree distribution is found to decay as a Poisson distribution when the entropy is maximized and to have a power-law tail with an exponent γ → 2 when the entropy is minimized.      

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.     

Detecting the optimal number of communities in complex networks

To obtain the optimal number of communities is an important problem in detecting community structures. In this paper, we use the extended measurement of community detecting algorithms to find the optimal community number. Based on the normalized mutual information index, which has been used as a measure for similarity of communities, a statistic Ω(c) is proposed to detect the optimal number of communities. In general, when Ω(c) reaches its local maximum, especially the first one, the corresponding number of communities c is likely to be optimal in community detection. Moreover, the statistic Ω(c) can also measure the significance of community structures in complex networks, which has been paid more attention recently. Numerical and empirical results show that the index Ω(c) is effective in both artificial and real world networks.     

Synchronization of time varying delayed complex networks via impulsive control

In this paper, we investigate the problem of synchronization for the time varying delayed complex dynamical networks via impulsive control method, several sufficient synchronization conditions are given, and we consider the impulsive control matrices are time varying delayed matrices. Furthermore, we found impulsive control does not always play an active role in synchronization although impulsive control strategy is cheaper and simpler than other control strategy. Finally, numerical simulations are also given to demonstrate the effectiveness of the proposed schemes.     

Dynamics of load entropy during cascading failure propagation in scale-free networks

In this Letter, we introduce the concept of load entropy, which can be an average measure of a network's heterogeneity in the load distribution. Then we investigate the dynamics of load entropy during failure propagation using a new cascading failures load model, which can represent the node removal mechanism in many real-life complex systems. Simulation results show that in the early stage of failure propagation the load entropy for a larger cascading failure increases more sharply than that for a smaller one, and consequently the cascading failure with a larger damage can be identified at the early stage of failure propagation according to the load entropy. Particularly, load entropy can be used as an index to be optimized in cascading failures control and defense in many real-life complex networks.     

基于通信序列熵的复杂网络传输容量

网络的传输性能在一定程度上依赖于网络的拓扑结构.本文从结构信息的角度分析复杂网络的传输动力学行为,寻找影响网络传输容量的信息结构测度指标.通信序列熵可以有效地量化网络的整体结构信息,为了表征网络整体传输能力,把通信序列熵引入到复杂网络传输动力学分析中,研究网络的通信序列熵与传输性能之间的关联特性,分析这种相关性存在的内在机理.分别在BA无标度和WS小世界网络模型上进行仿真,结果显示:网络的通信序列熵与其传输容量存在密切关联性,随着通信序列熵的增加,网络拓扑结构的均匀性随之增强,传输容量明显增加.网络的传输容量是通信序列熵的单调递增函数,与通信序列熵成正关联关系.通信序列熵可有效评估网络的传输容量,本结论可为设计高传输容量网络提供理论依据.     

Optimal dynamic bandwidth allocation for complex networks

Traffic capacity of one network strongly depends on the link’s bandwidth allocation strategy. In previous bandwidth allocation mechanisms, once one link’s bandwidth is allocated, it will be fixed throughout the overall traffic transmission process. However, the traffic load of every link changes from time to time. In this paper, with finite total bandwidth resource of the network, we propose to dynamically allocate the total bandwidth resource in which each link’s bandwidth is proportional to the queue length of the output buffer of the link per time step. With plenty of data packets in the network, the traffic handling ability of all links of the network achieves full utilization. The theoretical analysis and the extensive simulation results on complex networks are consistent. This work is valuable for network service providers to improve network performance or to do reasonable network design efficiently.