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EXTENDED clustering coefficientS：GENERALIZATION OF clustering coefficientS IN SMALL-WORLD NETWORKS

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Journal of Systems Science and Systems Engineering 2007年第3期16卷 370-382页

作者： Wenjun XIAO Wenhong WEI Weidong CHEN Yong QIN Behrooz PARHAMI Department of Computer Science South China University of Technology Guangzhou 510641 China Department of Electrical & ComputerEngineering University of California Santa Barbara CA 93106-9560 USA

The clustering coefficient C of a network, which is a measure of direct connectivity between neighbors of the various nodes, ranges from 0 （for no connectivity） to 1 （for full connectivity）. We define extended clustering coefficients C（h） of a small-world network based on nodes that are at distance h from a source node, thus generalizing distance-1 neighborhoods employed in computing the ordinary clustering coefficient C = C（1）. Based on known results about the distance distribution Pδ（h） in a network, that is, the probability that a randomly chosen pair of vertices have distance h, we derive and experimentally validate the law Pδ（h）C（h） ≤ c log N / N, where c is a small constant that seldom exceeds 1. This result is significant because it shows that the product Pδ（h）C（h） is upper-bounded by a value that is considerably smaller than the product of maximum values for Pδ（h） and C（h）. Extended clustering coefficients and laws that govern them offer new insights into the structure of small-world networks and open up avenues for further exploration of their properties.

关键词： clustering coefficient small-world extended clustering coefficient distance distribution

Evolutionary prisoner's dilemma game on highly clustered community networks

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Chinese Physics B 2009年第7期18卷 2623-2628页

作者：刘永奎李智陈小杰王龙 Center for Complex Systems Department of Automatic Control Engineering Xidian University State Key Laboratory for Turbulence and Complex Systems Center for Systems and Control College of Engineering Peking University

This paper studies the evolutionary prisoner＇s dilemma game on a highly clustered community network in which the clustering coefficient and the community size can be tuned. It finds that the clustering coefficient in such a degree-homogeneous network inhibits the emergence of cooperation for the entire range of the payoff parameter. Moreover, it finds that the community size can also have a marked influence on the evolution of cooperation, with a larger community size leading to not only a lower cooperation level but also a smaller threshold of the payoff parameter above which cooperators become extinct.

关键词： prisoner's dilemma cooperation clustering coefficient community structure

A novel evolving scale-free model with tunable attractiveness

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Chinese Physics B 2010年第7期19卷 35-39页

作者：刘绚刘天琪王昊李兴源 School of Electrical Engineering and Automation Sichuan University College of Electronics and Information Engineering Sichuan University

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.

关键词： scale-free tunable attractiveness degree distribution clustering coefficient

Synchronization in Triangled Complex Networks

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Communications in Theoretical Physics 2006年第5期45卷 955-960页

作者： LU Xin-Biao LI Xiang WANG xiao-Fan Department of Automation Shanghai Jiao Tong University Shanghai 200240 China China Institute of Atomic Energy P.O. Box 275-81 Beijing 102413 China

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.

关键词： synchronization weighted network clustering coefficient

Evolution of two properties for scale-free network

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Journal of Systems Engineering and Electronics 2006年第3期17卷 535-540页

作者： Li Shouwei Qian Xingsan School of Management Univ. of Shanghai for Science and Technology Shanghai 200093 P. R. of China

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.

关键词： fuzzy fitness clustering coefficient power law distribution scale-free.

An Ideal Assortative Network and Synchronization

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Communications in Theoretical Physics 2007年第1期47卷 186-192页

作者： DONG Cheng-Dong LIU Zeng-Rong Department of Applied Mathematics Shanghai University of Finance and Economics Shanghai 200433 China Institute of Systems Biology Shanghai University Shanghai 200444 China

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.

关键词： complex network assortative property average path length clustering coefficient synchronization

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

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Communications in Theoretical Physics 2009年第5期51卷 947-953页

作者： ZHANG Gui-Qing WANG Lin CHEN Tian-Lun Department of Physics Nankai University Tianjin 300071 China

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.

关键词： complex network evolving weighted network clustering coefficient weighted assortativity coefficient correlation

Online social network model with renewal and accelerated growth

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The Journal of China Universities of Posts and Telecommunications 2014年第4期21卷 54-63页

作者： WU Zhe GUO Yu-chun CHEN Chang-jia School of Electrical and Computer Engineering Beijing Jiaotong University

Based on observation of the growing mechanism in Twitter-like online social networks, an online social network （OSN） evolution model was proposed, a renewal mechanism for the old nodes and an accelerated growth mechanism was introduced for the new nodes, comparing with the native copying model. Topological characteristics of the generated networks, such as degree distribution, average shortest-path length and clustering coefficient, are analyzed and numerized. These properties are validated with some crawled datasets of real online social networks.

关键词： online social network network evolution model degree distribution average shortest-path length clustering coefficient

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

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Neural Regeneration Research 2018年第6期13卷 1061-1065页

作者： Wei-Wei Wang Ye-Chen Lu Wei-Jun Tang Jun-Hai Zhang Hua-Ping Sun Xiao-Yuan Feng Han-Qiu Liu Department of Radiology Huashan Hospital Fudan University Department of Hand Surgery Huashan Hospital Fudan University

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 *** in brain networks may help understanding of brain plasticity at the global *** hypothesized that topology of the global cerebral resting-state functional network changes after unilateral brachial plexus ***,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 *** correlation matrices were then converted into a binary matrix with affixed sparsity values of 0.1–*** sparsity conditions,both groups satisfied this small-world *** clustering coefficient was markedly lower,while average shortest path remarkably higher in patients compared with healthy *** 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 ***,varied small-worldness suggests that capacity of information transmission and integration in different brain regions in brachial plexus injury patients is damaged.

关键词： nerve regeneration brachial plexus injury functional magnetic resonance imaging small-world network small-world property topology properties functional reorganization clustering coefficient shortest path peripheral nerve injury neural regeneration