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.

Evolutionary prisoner's dilemma game on highly clustered community networks

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.

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.

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.

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.

EXTENDED CLUSTERING COEFFICIENTS：GENERALIZATION OF CLUSTERING COEFFICIENTS IN SMALL-WORLD NETWORKS

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.

Quasispecies distribution of Eigen model

We have studied sharp peak landscapes of the Eigen model from a new perspective about how the quasispecies are distributed in the sequence space. To analyse the distribution more carefully, we bring in two tools. One tool is the variance of Hamming distance of the sequences at a given generation. It not only offers us a different avenue for accurately locating the error threshold and illustrates how the configuration of the distribution varies with copying fidelity q in the sequence space, but also divides the copying fidelity into three distinct regimes. The other tool is the similarity network of a certain Hamming distance do, by which we can gain a visual and in-depth result about how the sequences axe distributed. We find that there are several local similarity optima around the centre （global similarity optimum） in the distribution of the sequences reproduced near the threshold. Furthermore, it is interesting that the distribution of clustering coefficient C（k） follows lognormal distribution and the curve of clustering coefficient C of the network versus do appears to be linear near the threshold.

Construction Research of Maintenance Support System

In order to guide the construction of maintenance support system,the theory of complex network to maintenance support area is introduced,and a construction idea of maintenance support system based on complex network is put forward.Firstly,from the perspective of the similarity,maintenance support system is abstracted into complex network to form maintenance support network.Secondly,the basic concepts and parameters of maintenance support network are also introduced.Thirdly,the maintenance support system in certain period is abstracted into a maintenance support network,and the network makes some changes.Finally,the correlative parameters of the network are calculated.The results show that the changed network is more conducive to the maintenance support.This provides a new thought and method to construct maintenance support system.

Integrating Local Closure Coefficient into Weighted Networks for Link Prediction

Triadic closure is a simple and fundamental kind of link formulation mechanism in network.Local closure coefficient(LCC),a new network property,is to measure the triadic closure with respect to the fraction of length-2 paths for link prediction.In this paper,a weighted format of LCC(WLCC)is introduced to measure the weighted strength of local triadic structure,and a statistic similari-ty-based link prediction metric is proposed to incorporate the definition of WLCC.To prove the metrics effectiveness and scalability,the WLCC formula-tion was further investigated under weighted local Naive Bayes(WLNB)link prediction framework.Finally,extensive experimental studies was conducted with weighted baseline metrics on various public network datasets.The results demonstrate the merits of the proposed metrics in comparison with the weighted baselines.

Nonpharmaceutical interventions contribute to the control of COVID-19 in China based on a pairwise model

Nonpharmaceutical interventions(NPIs),particularly contact tracing isolation and household quarantine,play a vital role in effectively bringing the Coronavirus Disease 2019(COVID-19)under control in China.The pairwise model,has an inherent advantage in characterizing those two NPIs than the classical well-mixed models.Therefore,in this paper,we devised a pairwise epidemic model with NPIs to analyze COVID-19 outbreak in China by using confirmed cases during February 3rde22nd,2020.By explicitly incorporating contact tracing isolation and family clusters caused by household quarantine,our model provided a good fit to the trajectory of COVID-19 infections.We calculated the reproduction number R=1.345(95%CI:1.230-1.460)for Hubei province and R=1.217(95%CI:1.207-1.227)for China(except Hubei).We also estimated the peak time of infections,the epidemic duration and the final size,which are basically consistent with real observation.We indicated by simulation that the traced high-risk contacts from incubated to susceptible decrease under NPIs,regardless of infected cases.The sensitivity analysis showed that reducing the exposure of the susceptible and increasing the clustering coefficient bolster COVID-19 control.With the enforcement of household quarantine,the reproduction number R and the epidemic prevalence declined effectively.Furthermore,we obtained the resumption time of work and production in China(except Hubei)on 10th March and in Hubei at the end of April 2020,respectively,which is broadly in line with the actual time.Our results may provide some potential lessons from China on the control of COVID-19 for other parts of the world.

Online social network model with renewal and accelerated growth

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.

Modeling the early transmission of COVID-19 in New York and San Francisco using a pairwise network model

Classical epidemiological models assume mass action.However,this assumption is violated when interactions are not random.With the recent COVID-19 pandemic,and resulting shelter in place social distancing directives,mass action models must be modified to account for limited social interactions.In this paper we apply a pairwise network model with moment closure to study the early transmission of COVID-19 in New York and San Francisco and to investigate the factors determining the severity and duration of outbreak in these two cities.In particular,we consider the role of population density,transmission rates and social distancing on the disease dynamics and outcomes.Sensitivity analysis shows that there is a strongly negative correlation between the clustering coefficient in the pairwise model and the basic reproduction number and the effective reproduction number.The shelter in place policy makes the clustering coefficient increase thereby reducing the basic reproduction number and the effective reproduction number.By switching population densities in New York and San Francisco we demonstrate how the outbreak would progress if New York had the same density as San Francisco and vice-versa.The results underscore the crucial role that population density has in the epidemic outcomes.We also show that under the assumption of no further changes in policy or transmission dynamics not lifting the shelter in place policy would have little effect on final outbreak size in New York,but would reduce the final size in San Francisco by 97%.

The effect of Internet separation degree time sensitivity on transmission

Separation degree is a standard measure for complex network research.Whatever its scale or its increase makes the Internet take on a complex network character.Because of the development of complex network theory and the continuous evolution of the Internet,it is a key problem that uses complex network theory to research the Internet nowadays.In this paper,the Internet separation degree is put forward.The time series stochastic process model of the Internet separation degree is established.According to ac-tual data,the Internet separation degree time sensitivity model(ISDTSM)is established and the effect of time sensi-tivity of the Internet separation degree to the Internet IP level transmission is computed.Finally the Internet separa-tion and IP transmission during 2008 Beijing Olympic Games were forecasted by using the model.