Evolution of two properties for scale-free network

Fitness of node can denote its competing power and clustering denotes the transitivity of network. Because the fitness of node is uncertain or fuzzy in some social networks, an explicit form of the degree distribution on fuzzy fitness is derived within a mean field approach. It is a weighted sum of different fuzzy fitness. It can be found that the fuzzy fitness of nodes may lead to multiscaling. Moreover, the clustering coefficient of node decays as power law and clustering coefficient of network behavior not-decrease-but-increase’ phenomenon after some time. Some computer simulation results of these models illustrate these analytical results.

Flat-head power-law, size-independent clustering, and scaling of coevolutionary scale-free networks

Scale-free topology and high clustering coexist in some real networks, and keep invariant for growing sizes of the systems. Previous models could hardly give out size-independent clustering with self- organized mechanism when succeeded in producing power-law degree distributions. Always ignored, some empirical statistic results display flat-head power-law behaviors. We modify our recent coevo- lutionary model to explain such phenomena with the inert property of nodes to retain small portion of unfavorable links in self-organized rewiring process. Flat-head power-law and size-independent clustering are induced as the new characteristics by this modification. In addition, a new scaling relation is found as the result of interplay between node state growth and adaptive variation of connections.

Exact Solution for Clustering Coefficient of Random Apollonian Networks

By means of the series method, we obtain the exact analytical solution of clustering coefficient in random Apollonian networks [Phys. Rev. E 71 （2005）046141]. Our exact analytical result is identical with the simulation, whereas in the original work, there is a deviation of about 4% between their approximate analytical result and the simulation.

Effects of Inter-Particle Frictional Coefficients on Evolution of Contact Networks in Landslide Process

During the process of landslide, its dynamic mechanism is important to understand and predict these kinds of natural hazard. In this paper, a new method, based on concepts of complex networks, has been proposed to investigate the evolution of contact networks in mesoscale during the sliding process of slope. A slope model was established using the discrete element method (DEM), and influences of inter-particle frictional coefficients with four different values on?dynamic landslides were studied. Both macroscopic analysis on slope?landslide?and mesoanalysis on structure evolution of contact networks, including the?average degree, clustering coefficient?and N-cycle, were done during the process?of landslide. The analysis results demonstrate that: 1) with increasing inter-particle?frictional coefficients, the displacement of slope decreases and the stable angle of slope post-failure increases, which is smaller than the peak internal frictional angle;2) the average degree decreases with the increase of inter-particle frictional coefficient. When the displacement at the toe of the slope is smaller,?the average degree there changes more greatly with increasing inter-particle?frictional coefficient;3) during the initial stage of landslide, the clustering coefficient?reduces sharply, which may leads to easily slide of slope. As the landslide?going?on, however, the clustering coefficient?increases denoting increasing stability?with?increasing inter-particle frictional coefficients. When the inter-particle?frictional coefficient is smaller than 0.3, its variation can affect the clustering coefficient?and stable inclination of slope post-failure greatly;and 4) the number of?3-cycle increases, but 4-cycle and 5-cycle decrease with increasing inter-particle frictional coefficients.

A novel evolving scale-free model with tunable attractiveness

In this paper, a new evolving model with tunable attractiveness is presented. Based on the Barabasi-Albert （BA） model, we introduce the attractiveness of node which can change with node degree. Using the mean-field theory, we obtain the analytical expression of power-law degree distribution with the exponent γ∈ （3, ∞）. The new model is more homogeneous and has a lower clustering coefficient and bigger average path length than the BA model.

基于高阶信息的网络相似性比较方法

量化复杂网络之间的结构相似性是网络科学中一个基本且具有挑战性的问题,在医学、社会学等多个领域发挥了至关重要的作用.传统的网络比较方法通常基于简单的结构特征,例如节点度分布、最短路径长度等,这些方法可能无法充分捕捉网络的全局结构信息,导致得到的网络相似性不精准.本文提出了一种基于高阶信息的网络相似性比较方法,该方法同时考虑了网络的全局结构和局部结构.具体而言,通过构建网络节点的高阶聚类系数分布和节点间距离分布,并利用基于这两个分布的Jensen-Shannon散度来量化网络之间的相似性.实验结果表明,相较于其他基线方法,本文提出的方法不仅能高效地比较不同网络的相似性,且在对真实网络进行扰动的过程中也表现出鲁棒性.

基于复杂网络理论的地铁网络鲁棒性研究

地铁网络作为现代城市交通的重要组成部分,其运行的可靠性和稳定性对于城市的正常运转至关重要。然而,地铁网络可能面临各种干扰和故障,如设备故障、自然灾害、人为破坏等,可能导致线路中断、列车延误和乘客服务中断。因此,研究地铁网络的鲁棒性,即系统在面对这些干扰时的恢复能力,对于提高地铁网络的可靠性和抗干扰性具有重要意义。文章基于复杂网络理论,综合考虑地铁网络的拓扑结构、节点重要性和客流分布等因素,对地铁网络的鲁棒性进行定量分析。研究采用Space-L方法对杭州市地铁网络拓扑结构特性进行分析,并分析了网络的度、介数、聚类系数和最短路径长度等网络特性指标。针对鲁棒性分析,文章采用了随机攻击和蓄意攻击的9种不同攻击策略,并对杭州市地铁网络进行实例分析。研究结果表明,关键指标的变化对地铁网络的鲁棒性产生显著影响。通过分析不同攻击策略下的网络性能指标,可以揭示系统中的脆弱节点和脆弱路径。这些分析结果对于提高杭州市地铁网络的鲁棒性,增强其对干扰和攻击的抵抗能力具有重要意义。

Small-worldness of brain networks after brachial plexus injury: a resting-state functional magnetic resonance imaging study

Research on brain function after brachial plexus injury focuses on local cortical functional reorganization,and few studies have focused on brain networks after brachial plexus injury.Changes in brain networks may help understanding of brain plasticity at the global level.We hypothesized that topology of the global cerebral resting-state functional network changes after unilateral brachial plexus injury.Thus,in this cross-sectional study,we recruited eight male patients with unilateral brachial plexus injury（right handedness,mean age of 27.9±5.4years old）and eight male healthy controls（right handedness,mean age of 28.6±3.2）.After acquiring and preprocessing resting-state magnetic resonance imaging data,the cerebrum was divided into 90 regions and Pearson’s correlation coefficient calculated between regions.These correlation matrices were then converted into a binary matrix with affixed sparsity values of 0.1–0.46.Under sparsity conditions,both groups satisfied this small-world property.The clustering coefficient was markedly lower,while average shortest path remarkably higher in patients compared with healthy controls.These findings confirm that cerebral functional networks in patients still show smallworld characteristics,which are highly effective in information transmission in the brain,as well as normal controls.Alternatively,varied small-worldness suggests that capacity of information transmission and integration in different brain regions in brachial plexus injury patients is damaged.

Resting-state network complexity and magnitude changes in neonates with severe hypoxic ischemic encephalopathy

Resting-state functional magnetic resonance imaging has revealed disrupted brain network connectivity in adults and teenagers with cerebral palsy. However, the specific brain networks implicated in neonatal cases remain poorly understood. In this study, we recruited 14 termborn infants with mild hypoxic ischemic encephalopathy and 14 term-born infants with severe hypoxic ischemic encephalopathy from Changzhou Children's Hospital, China. Resting-state functional magnetic resonance imaging data showed efficient small-world organization in whole-brain networks in both the mild and severe hypoxic ischemic encephalopathy groups. However, compared with the mild hypoxic ischemic encephalopathy group, the severe hypoxic ischemic encephalopathy group exhibited decreased local efficiency and a low clustering coefficient. The distribution of hub regions in the functional networks had fewer nodes in the severe hypoxic ischemic encephalopathy group compared with the mild hypoxic ischemic encephalopathy group. Moreover, nodal efficiency was reduced in the left rolandic operculum, left supramarginal gyrus, bilateral superior temporal gyrus, and right middle temporal gyrus. These results suggest that the topological structure of the resting state functional network in children with severe hypoxic ischemic encephalopathy is clearly distinct from that in children with mild hypoxic ischemic encephalopathy, and may be associated with impaired language, motion, and cognition. These data indicate that it may be possible to make early predictions regarding brain development in children with severe hypoxic ischemic encephalopathy, enabling early interventions targeting brain function. This study was approved by the Regional Ethics Review Boards of the Changzhou Children's Hospital(approval No. 2013-001) on January 31, 2013. Informed consent was obtained from the family members of the children. The trial was registered with the Chinese Clinical Trial Registry(registration number: ChiCTR1800016409) and the protocol version is 1.0.

The Clustering Coefficient and the Diameter of Small-world Networks

The small-world network, proposed by Watts and Strogatz, has been extensively studied for the past over ten years. In this paper, a generalized smMl-world network is proposed, which extends severM small-world network models. Furthermore, some properties of a special type of generalized small-world network with given expectation of edge numbers have been investigated, such as the degree distribution and the isoperimetric number. These results are used to present a lower and an upper bounds for the clustering coefficient and the diameter of the given edge number expectation generalized small-world network, respectively. In other words, we prove mathematically that the given edge number expectation generalized small-world network possesses large clustering coefficient and small diameter.

Hierarchy property of traffic networks

The flourishing complex network theory has aroused increasing interest in studying the properties of real-world networks. Based on the traffic network of Chang-Zhu Tan urban agglomeration in central China, some basic network topological characteristics were computed with data collected from local traffic maps, which showed that the traffic networks were small-world networks with strong resilience against failure; more importantly, the investigations of as- sortativity coefficient and average nearestlneighbour degree implied the disassortativity of the traffic networks. Since traffic network hierarchy as an important basic property has been neither studied intensively nor proved quantitatively, the authors are inspired to analyse traffic network hierarchy with disassortativity and to finely characterize hierarchy in the traffic networks by using the n-degree-n-clustering coefficient relationship. Through numerical results and analyses an exciting conclusion is drawn that the traffic networks exhibit a significant hierarchy, that is, the traffic networks are proved to be hierarchically organized. The result provides important information and theoretical groundwork for optimal transport planning.

A Mixed Mechanism of Weighted-Driven and Inner Selection in Networks

For most networks, the weight of connection is changing with their attachment and inner affinity. By introducing a mixed mechanism of weighted-driven and inner selection, the model exhibits wide range power-law distributions of node strength and edge weight, and the exponent can be adjusted by not only the parameter δ but also the probability q. Furthermore, we investigate the weighted average shortest distance, clustering coefficient, and the correlation of our network. In addition, the weighted assortativity coefficient which characterizes important information of weighted topological networks has been discussed, but the variation of coefficients is much smaller than the former researches.

An Ideal Assortative Network and Synchronization

This paper proposes a novel complex network with assortative property based on multi-center networks. The average path length and clustering coefficient of the network are calculated, and the impact on the network topology is investigated. A simple dynamic system established on the proposed network is used to analyze how the assortative property of the network affects synchronization.

Synchronization in Triangled Complex Networks

Using a tunable clustering coeffcient model withoutchanging the degree distribution, we investigate the effect of clustering coefficient on synchronization of networks with both unweighted and weighted couplings. For several typical categories of complex networks, the more triangles are in the networks, the worse the synchronizability of the networks is.

Three vertex degree correlations of fixed act-size collaboration networks

A rate equation approach was presented for the exact computation of the three vertex degree correlations of the fixed act-size collaboration networks.Measurements of the three vertex degree correlations were based on a rate equation in the continuous degree and time approximation for the average degree of the nearest neighbors of vertices of degree k,with an appropriate boundary condition.The rate equation proposed can be generalized in more sophisticated growing network models,and also extended to deal with related correlation measurements.Finally,in order to check the theoretical prediction,a numerical example was solved to demonstrate the performance of the degree correlation function.

Identifying Functional Modules in Complex Networks

In this paper, we propose a new method that enables us to detect and describe the functional modules in complex networks. Using the proposed method, we can classify the nodes of networks into different modules according to their pattern of intra- and extra-module links. We use our method to analyze the modular structures of the ER random networks. We find that different modules of networks have different structure properties, such as the clustering coefficient. Moreover, at the same time, many nodes of networks participate different modules. Remarkably, we find that in the ER random networks, when the probability p is small, different modules or different roles of nodes can be Mentified by different regions in the c-p parameter space.

On the Dynamical Analysis in Aftershock Networks

We investigate the dynamical behavior of aftershocks in earthquake networks, and the earthquake network calculated from a time series is constructed by contemplating cell resolution and temporal causality. We attempt to connect an earthquake network using relationship between one main earthquake and its aftershocks from seismic data of California. We mainly examine some topological properties of the earthquake such as the degree distribution, the characteristic path length, the clustering coefficient, and the global efficiency. Our result cannot presently determine the universal scaling exponents in statistical quantities, but the topological properties may be inferred to advance and improve by implementing the method and its technique of networks. Particularly, it may be dealt with a network issue of convenience and of importance in the case how large networks construct in time to proceed on earthquake systems.

不同聚类系数无标度脉冲神经网络动态特性对比分析

拓扑结构可以影响脉冲神经网络的功能。聚类系数是反映网络连通性的重要拓扑性质之一,基于不同聚类系数拓扑进行脉冲神经网络的研究对于进一步理解网络拓扑性质对网络功能影响具有重要意义。以Izhikevich神经元模型为节点,突触可塑性为边,分别构建高、低聚类系数无标度拓扑的脉冲神经网络,评估并对比两种网络的动态特性。实验结果表明,两种网络动态特性随时间均先剧烈变化而后逐渐趋于稳定;在网络连接强度、局部和全局信息传输效率、小世界属性方面,高聚类均比低聚类无标度脉冲神经网络更具优势。