我们学习消息在一个没有规模的网络上传播,由介绍新奇忘记记得机制。消息,能指电子邮件的一个一般术语,新闻,谣言或疾病,等等,能被它的持有者忘记并且记得。消息被忘记并且记得的方法被 forget 管理并且分别地记得功能, F 和 R...我们学习消息在一个没有规模的网络上传播,由介绍新奇忘记记得机制。消息,能指电子邮件的一个一般术语,新闻,谣言或疾病,等等,能被它的持有者忘记并且记得。消息被忘记并且记得的方法被 forget 管理并且分别地记得功能, F 和 R。F 和 R 是有关个人的家的历史时间 t 的功能以前的状态,也就是是活跃的(与消息) 或不活跃(没有消息) 。我们以传播能是有效的低传播率的系统的模拟表演被相应参数首先为 F 和 R 决定。展开更多
It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular l...It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular lattices. Although these features capture the important characteristics of complex networks, their applicability depends on the style of networks. To unravel the universal characteristics many complex networks have in common, we study the fractal dimensions of complex networks using the method introduced by Shanker. We find that the average 'density' (p(r ) ) of complex networks follows a better power-law function as a function of distance r with the exponent dl, which is defined as the fractal dimension, in some real complex networks. Furthermore, we study the relation between df and the shortcuts Nadd in small-world networks and the size N in regular lattices. Our present work provides a new perspective to understand the dependence of the fractal dimension df on the complex network structure.展开更多
The air transportation network, one of the common multilayer complex systems, is composed of a collection of individual airlines, and each airline corresponds to a different layer. An important question is then how ma...The air transportation network, one of the common multilayer complex systems, is composed of a collection of individual airlines, and each airline corresponds to a different layer. An important question is then how many airlines are really necessary to represent the optimal structure of a multilayer air transportation system. Here we take the Chinese air transportation network (CATN) as an example to explore the nature of multiplex systems through the procedure of network aggregation. Specifically, we propose a series of structural measures to characterize the CATN from the multilayered to the aggregated network level. We show how these measures evolve during the network aggregation process in which layers are gradually merged together and find that there is an evident structural transition that happened in the aggregated network with nine randomly chosen airlines merged, where the network features and construction cost of this network are almost equivalent to those of the present CATN with twenty-two airlines under this condition. These findings could shed some light on network structure optimization and management of the Chinese air transportation system.展开更多
Many systems can display a very short,rapid changing stage(quasi-discontinuous region)inside a relatively very long and slowly changing process.A quantitative definition for the"quasi-discontinuity"in these ...Many systems can display a very short,rapid changing stage(quasi-discontinuous region)inside a relatively very long and slowly changing process.A quantitative definition for the"quasi-discontinuity"in these systems has been introduced.We have shown by a simplified model that extra-large Feigenbaum constants can be found inside some period-doubling cascades due to the quasi-discontinuity.As an example,this phenomenon has also been observed in Rose-Hindmash model describing neuron activities.展开更多
In a two-dimensional area-preserving map we found a kind of noninvertibility that is induced by a piece-wise smooth property of the map.This can lead to the appearance of such kinds of elliptic islands that attract th...In a two-dimensional area-preserving map we found a kind of noninvertibility that is induced by a piece-wise smooth property of the map.This can lead to the appearance of such kinds of elliptic islands that attract the iterations from a set of initial values outside themselves,while behaving regularly inside.We suggest calling such islands quasi-attractors.展开更多
我们建议一个模型在对小世界网络的一个外部领域的影响下面学习意见的进化。代理人的意见和时间过去的相对变化率的宏行为被学习。外部领域被发现在造成意见 s (t) 平衡或增加起一个重要作用,并且没有外部领域的影响,相对变化率鲸鱼群...我们建议一个模型在对小世界网络的一个外部领域的影响下面学习意见的进化。代理人的意见和时间过去的相对变化率的宏行为被学习。外部领域被发现在造成意见 s (t) 平衡或增加起一个重要作用,并且没有外部领域的影响,相对变化率鲸鱼群妈(t) 表演时间跑的非线性的增加行为。而且,这非线性的增加行为独立于起始的条件,外部领域的力量和我们取消外部领域的时间。结果可以在我们的社会反映一些现象,例如在中国的宏控制或在我们的社会的大众媒体的功能。展开更多
We introduce variant rates,for both infection and recovery and noise into the susceptible-infected-removed(SIR)modelfor epidemic spreading.The changing rates are taken mainly due to the changing profiles of an epidemi...We introduce variant rates,for both infection and recovery and noise into the susceptible-infected-removed(SIR)modelfor epidemic spreading.The changing rates are taken mainly due to the changing profiles of an epidemic during its evolution.However,the noise parameter which is taken from a given distribution,i.e.Gaussian can describe the fluctuations of the infection and recovery rates.The numerical simulations show that the SIR model with variant rates and noise and can improve the fitting with real SARS data in the near-stationary stage.展开更多
A remarkable phenomenon in the time evolution of many networks such as cultural,political,national and economic systems is the recurrent transition between the states of union and the division of nodes.We propose a ph...A remarkable phenomenon in the time evolution of many networks such as cultural,political,national and economic systems is the recurrent transition between the states of union and the division of nodes.We propose a phenomenological modeling,inspired by the maxim"long union divides and long division unites"to investigate the evolutionary characters of these networks composed of the entities whose behaviors are dominated by these two events.The nodes are endowed with quantities such as identity,ingredient,richness(power),openness(connections),age,distance,and interaction,which determine collectively the evolution in a probabilistic way.Depending on a tunable parameter,the time evolution of this model is mainly an alternative domination of union or division state,with a possible state of final union dominated by one single node.展开更多
Different types of models for describing the motion of a kicked ion were suggested and studied. It is shown that certain kinds of jumping behavior of the exerting electromagnetic field can lead to a type of noninverti...Different types of models for describing the motion of a kicked ion were suggested and studied. It is shown that certain kinds of jumping behavior of the exerting electromagnetic field can lead to a type of noninvertible property, which changes this conservative system into a 'quasi-dissipative' one. The quasi-dissipative behaviors allow the particle to move along a confined chaotic 'quasi-attractor' in many regions of the parameter space. If the exerting electromagnetic field is discontinuous but the system is still invertible, it will take an unbounded chaotic diffusion with similar parameter values. We hope that this discovery could provide a helpful idea for confining the plasma.展开更多
<Abstract>English and Chinese language frequency time series (LFTS) were constructed based on an English and two Chinese novels. Methods of statistical hypothesis testing were adopted to test the nonlinear prope...<Abstract>English and Chinese language frequency time series (LFTS) were constructed based on an English and two Chinese novels. Methods of statistical hypothesis testing were adopted to test the nonlinear properties of the LFTS. Results suggest the series exhibited non-normal, auto-correlative, and stationary characteristics. Moreover, we found that LFTS follow the power law distributions, and thereby we investigated the fractal structure, long range correlation, and intermittency, which indicated the self-similarity features of LFTS, and also provided hints that human societies are likely to share some universal properties.展开更多
A first-principles derivation is presented of canonical distributions for a finite thermostat taking into account nonextensive energy. Parameterizing this energy by λ , we derive an explicit form for the distribution...A first-principles derivation is presented of canonical distributions for a finite thermostat taking into account nonextensive energy. Parameterizing this energy by λ , we derive an explicit form for the distribution functions by regulating λ , and then explore the nontrivial relationship between these functions and energy nonextensivity, as well other system parameters such as system size. A variational entropy function is also derived from these distribution functions.展开更多
Two kinds of noise strategies in binary opinion dynamics on ER random networks are discussed. Random noise p1 in the initial configuration plays a role in redistributing the opinion states associated with the network....Two kinds of noise strategies in binary opinion dynamics on ER random networks are discussed. Random noise p1 in the initial configuration plays a role in redistributing the opinion states associated with the network. Under synchronous updating, the system can attain a stable state within few time steps. The fraction of nodes with changed opinion states F decreases exponentially with time, and the ratio of one of the two opinion states R remains almost unchanged during the evolution. The average ratio <R> crosses at the half-half initial concentration under different p1. For noise in the dynamical evolution p2, the system can reach a steady state with small fluctuations. With larger p2, more nodes have changed opinion states at each updating and more nodes with opposite opinions coexist. If p2 is greater than 0.5, the two opinions coexist with equal support.展开更多
We propose a mean-field Bak-Sneppen (MFBS) model with varying interaction strength. The interaction strength, here denoted by α, specifies the degree of interaction, and varies smoothly between 0 for no interaction a...We propose a mean-field Bak-Sneppen (MFBS) model with varying interaction strength. The interaction strength, here denoted by α, specifies the degree of interaction, and varies smoothly between 0 for no interaction and 1 for full interaction (restoring the original BS model). Our simulations of the MFBS model reveal some interesting features. When α is non-zero, the MFBS model can evolve to a self-organized critical (SOC) state. The critical exponent of the avalanche size distribution, α, is insensitive to changes in α. The critical exponent of average avalanche size, α, and the avalanche dimension exponent, D, both increase slightly with α < 0.5 but remain constant if α > 0.5. The critical threshold fc decreases almost linearly with α.展开更多
We construct a weighted network of scientific collaboration in computational geometry and study the statistical properties of the network. In addition, we introduce a parameter called the collaboration relationship pa...We construct a weighted network of scientific collaboration in computational geometry and study the statistical properties of the network. In addition, we introduce a parameter called the collaboration relationship parameter to measure the collaboration between scientists. The collaboration relationship parameter of two scientists depends not only on the connection weights between the nodes, but also on the network's structure. The stability of the network's structure in terms of different edge removal strategies is also studied. According to the parameter, we find that a community structure exists in this type of network.展开更多
In this paper,we propose a simple model of opinion dynamics to construct social networks,based on the algorithm of link rewiring of local attachment(RLA)and global attachment(RGA).Generality,the system does reach a st...In this paper,we propose a simple model of opinion dynamics to construct social networks,based on the algorithm of link rewiring of local attachment(RLA)and global attachment(RGA).Generality,the system does reach a steady state where all individuals'opinion and the complex network structure are fixed.The RGA enhances the ability of consensus of opinion formation.Furthermore,by tuning a model parameter p,which governs the proportion of RLA and RGA,we find the formation of hierarchical structure in the social networks for p>p_(c).Here,p_(c) is related to the complex network size N and the minimal coordination number 2K.The model also reproduces many features of large social networks,including the“weak links”property.展开更多
Spatial distance has a remarkable effect on the attended mode of a network embedded in a certain space. First, we investigate how spatial restriction leads to information-information correlation that is strong, linear...Spatial distance has a remarkable effect on the attended mode of a network embedded in a certain space. First, we investigate how spatial restriction leads to information-information correlation that is strong, linear and positive in real networks. We then construct a two-dimensional space, define the action radius R for nodes of networks, and propose a class of models that depend on spatial distance. Information correlation of the models is consistent with that of real networks. The spatial distance plays a leading role in generating assortative mixing by degree, while the generation of disassortative mixing relies on both the degree of preferential attachment and spatial restriction.展开更多
Motivated by the need to include the different characteristics of individuals and the damping effect in predictions of epidemic spreading, we build a model with variant coefficients and white Gaussian noise based on t...Motivated by the need to include the different characteristics of individuals and the damping effect in predictions of epidemic spreading, we build a model with variant coefficients and white Gaussian noise based on the traditional SIR model. The analytic and simulation results predicted by the model are presented and discussed. The simulations show that using the variant coefficients results in a higher percentage of susceptible individuals and a lower percentage of removed individuals. When the noise is included in the model, the percentage of infected individuals has a wider peak and more fluctuations than that predicted using the traditional SIR model.展开更多
Varentropy is used as a general measure of probabilistic uncertainty for a complex network, inspired by the first and second laws of thermodynamics, but not limited to the equilibrium system. By exploring the relation...Varentropy is used as a general measure of probabilistic uncertainty for a complex network, inspired by the first and second laws of thermodynamics, but not limited to the equilibrium system. By exploring the relationship between the varentropy of the scale free distribution and the exponent of power laws as well as network size, we get the optimal design of a scale-free network against random failures. The behaviors of varentropy and the Shannon entropy of double Pareto law degree distribution are analyzed to compare their usefulness. Our conclusion is that varentropy is suitable and reliable.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 70571027, 10647125, 10635020 and 70401020, and the Program of Introducing Talents of Discipline to Universities under Grant No B08033.
基金Supported in part by the National Natural Science Foundation of China under Grant Nos 70401020, 70571027, 10647125 and 10635020, and the Ministry of Education of China under Grant No 306022, and the 111 Project under Grant No B08033.
文摘我们学习消息在一个没有规模的网络上传播,由介绍新奇忘记记得机制。消息,能指电子邮件的一个一般术语,新闻,谣言或疾病,等等,能被它的持有者忘记并且记得。消息被忘记并且记得的方法被 forget 管理并且分别地记得功能, F 和 R。F 和 R 是有关个人的家的历史时间 t 的功能以前的状态,也就是是活跃的(与消息) 或不活跃(没有消息) 。我们以传播能是有效的低传播率的系统的模拟表演被相应参数首先为 F 和 R 决定。
基金Supported by the National Natural Science Foundation of China under Grant No 10635020,the Program of Introducing Talents of Discipline to Universities under Grant No B08033, the National Key Basic Research Program of China under Grant No 2008CB317106, and the Key Project of the Ministry of Education of China (306022 and IRT0624).
文摘It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular lattices. Although these features capture the important characteristics of complex networks, their applicability depends on the style of networks. To unravel the universal characteristics many complex networks have in common, we study the fractal dimensions of complex networks using the method introduced by Shanker. We find that the average 'density' (p(r ) ) of complex networks follows a better power-law function as a function of distance r with the exponent dl, which is defined as the fractal dimension, in some real complex networks. Furthermore, we study the relation between df and the shortcuts Nadd in small-world networks and the size N in regular lattices. Our present work provides a new perspective to understand the dependence of the fractal dimension df on the complex network structure.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11405118,11401448 and 11301403
文摘The air transportation network, one of the common multilayer complex systems, is composed of a collection of individual airlines, and each airline corresponds to a different layer. An important question is then how many airlines are really necessary to represent the optimal structure of a multilayer air transportation system. Here we take the Chinese air transportation network (CATN) as an example to explore the nature of multiplex systems through the procedure of network aggregation. Specifically, we propose a series of structural measures to characterize the CATN from the multilayered to the aggregated network level. We show how these measures evolve during the network aggregation process in which layers are gradually merged together and find that there is an evident structural transition that happened in the aggregated network with nine randomly chosen airlines merged, where the network features and construction cost of this network are almost equivalent to those of the present CATN with twenty-two airlines under this condition. These findings could shed some light on network structure optimization and management of the Chinese air transportation system.
基金Supported by the National Natural Science Foundation of China under Grant No.19975039the Foundation of Jiangsu Provincial Education Committee under the Grant No.98kjb140006.
文摘Many systems can display a very short,rapid changing stage(quasi-discontinuous region)inside a relatively very long and slowly changing process.A quantitative definition for the"quasi-discontinuity"in these systems has been introduced.We have shown by a simplified model that extra-large Feigenbaum constants can be found inside some period-doubling cascades due to the quasi-discontinuity.As an example,this phenomenon has also been observed in Rose-Hindmash model describing neuron activities.
基金Supported by the National Natural Science Foundation of China under Grant Nos.19975039,49474216 and 59876093the Natural Science Foundation of Jiangsu Provincial Education Committee under Grant No.98kjb140006the Chinese National Basic Research Climbing Project.
文摘In a two-dimensional area-preserving map we found a kind of noninvertibility that is induced by a piece-wise smooth property of the map.This can lead to the appearance of such kinds of elliptic islands that attract the iterations from a set of initial values outside themselves,while behaving regularly inside.We suggest calling such islands quasi-attractors.
基金Supported by the National Natural Science Foundation of China under grant Nos 70571027, 70401020, 10647125 and 10635020, and the Ministry of Education of China under Grant No 306022.
文摘我们建议一个模型在对小世界网络的一个外部领域的影响下面学习意见的进化。代理人的意见和时间过去的相对变化率的宏行为被学习。外部领域被发现在造成意见 s (t) 平衡或增加起一个重要作用,并且没有外部领域的影响,相对变化率鲸鱼群妈(t) 表演时间跑的非线性的增加行为。而且,这非线性的增加行为独立于起始的条件,外部领域的力量和我们取消外部领域的时间。结果可以在我们的社会反映一些现象,例如在中国的宏控制或在我们的社会的大众媒体的功能。
基金Supported by the National Natural Science Foundation of China under Grant Nos 70401020, 70571027, 10647125, and 10635020, and the Ministry of Education of China under Grant No 306022.
基金Supported in part by the National Natural Science Foundation of China under Grant Nos 10647125,10635020,10975057 and 10975062the Program of Introducing Talents of Discipline to Universities under Grant No B08033.GU Jiao is supported by Max-Planck-Institute for Mathematics in the Sciences。
文摘We introduce variant rates,for both infection and recovery and noise into the susceptible-infected-removed(SIR)modelfor epidemic spreading.The changing rates are taken mainly due to the changing profiles of an epidemic during its evolution.However,the noise parameter which is taken from a given distribution,i.e.Gaussian can describe the fluctuations of the infection and recovery rates.The numerical simulations show that the SIR model with variant rates and noise and can improve the fitting with real SARS data in the near-stationary stage.
文摘A remarkable phenomenon in the time evolution of many networks such as cultural,political,national and economic systems is the recurrent transition between the states of union and the division of nodes.We propose a phenomenological modeling,inspired by the maxim"long union divides and long division unites"to investigate the evolutionary characters of these networks composed of the entities whose behaviors are dominated by these two events.The nodes are endowed with quantities such as identity,ingredient,richness(power),openness(connections),age,distance,and interaction,which determine collectively the evolution in a probabilistic way.Depending on a tunable parameter,the time evolution of this model is mainly an alternative domination of union or division state,with a possible state of final union dominated by one single node.
基金the National Natural Foundation of China under Grant No. 19975039.
文摘Different types of models for describing the motion of a kicked ion were suggested and studied. It is shown that certain kinds of jumping behavior of the exerting electromagnetic field can lead to a type of noninvertible property, which changes this conservative system into a 'quasi-dissipative' one. The quasi-dissipative behaviors allow the particle to move along a confined chaotic 'quasi-attractor' in many regions of the parameter space. If the exerting electromagnetic field is discontinuous but the system is still invertible, it will take an unbounded chaotic diffusion with similar parameter values. We hope that this discovery could provide a helpful idea for confining the plasma.
基金supported by the National Natural Science Foundation of China (10647125, 10635020, 10975057 and 10975062)the Program of Introducing Talents of Discipline to Universities (B08033)the PHC CAI YUAN PEI Program (LIU JIN OU [2010] No. 6050) (2010008104)
文摘<Abstract>English and Chinese language frequency time series (LFTS) were constructed based on an English and two Chinese novels. Methods of statistical hypothesis testing were adopted to test the nonlinear properties of the LFTS. Results suggest the series exhibited non-normal, auto-correlative, and stationary characteristics. Moreover, we found that LFTS follow the power law distributions, and thereby we investigated the fractal structure, long range correlation, and intermittency, which indicated the self-similarity features of LFTS, and also provided hints that human societies are likely to share some universal properties.
基金supported by the National Natural Science Foundation of China (10647125, 10635020, 10975057, 10975062)the Program of Introducing Talents of Discipline to Universities (B08033)
文摘A first-principles derivation is presented of canonical distributions for a finite thermostat taking into account nonextensive energy. Parameterizing this energy by λ , we derive an explicit form for the distribution functions by regulating λ , and then explore the nontrivial relationship between these functions and energy nonextensivity, as well other system parameters such as system size. A variational entropy function is also derived from these distribution functions.
基金supported in part by the National Natural Science Founda-tion of China (10635020 and 10975057)the Ministry of Education of China (306022)
文摘Two kinds of noise strategies in binary opinion dynamics on ER random networks are discussed. Random noise p1 in the initial configuration plays a role in redistributing the opinion states associated with the network. Under synchronous updating, the system can attain a stable state within few time steps. The fraction of nodes with changed opinion states F decreases exponentially with time, and the ratio of one of the two opinion states R remains almost unchanged during the evolution. The average ratio <R> crosses at the half-half initial concentration under different p1. For noise in the dynamical evolution p2, the system can reach a steady state with small fluctuations. With larger p2, more nodes have changed opinion states at each updating and more nodes with opposite opinions coexist. If p2 is greater than 0.5, the two opinions coexist with equal support.
基金supported by the National Natural Science Foundation of China (10647125, 10635020, 10975057 and 10975062)the Program of Introducing Talents of Discipline to Universities (B08033)the Max-Planck-Institute for Mathematics in the Sciences
文摘We propose a mean-field Bak-Sneppen (MFBS) model with varying interaction strength. The interaction strength, here denoted by α, specifies the degree of interaction, and varies smoothly between 0 for no interaction and 1 for full interaction (restoring the original BS model). Our simulations of the MFBS model reveal some interesting features. When α is non-zero, the MFBS model can evolve to a self-organized critical (SOC) state. The critical exponent of the avalanche size distribution, α, is insensitive to changes in α. The critical exponent of average avalanche size, α, and the avalanche dimension exponent, D, both increase slightly with α < 0.5 but remain constant if α > 0.5. The critical threshold fc decreases almost linearly with α.
基金supported by the National Natural Science Foundation of China (10647125, 10635020, 10975057 and 10975062)the Program of Introducing Talents of Discipline to Universities (B08033)the PHC CAI YUAN PEI Program (LIU JIN OU [2010] No. 6050)
文摘We construct a weighted network of scientific collaboration in computational geometry and study the statistical properties of the network. In addition, we introduce a parameter called the collaboration relationship parameter to measure the collaboration between scientists. The collaboration relationship parameter of two scientists depends not only on the connection weights between the nodes, but also on the network's structure. The stability of the network's structure in terms of different edge removal strategies is also studied. According to the parameter, we find that a community structure exists in this type of network.
基金supported by the National Natural Science Foundation of China(Grant Nos.10647125,10635020,10975057 and 10975062)the Programme of Introducing Talents of Discipline to Universities under Grant No.B08033.
文摘In this paper,we propose a simple model of opinion dynamics to construct social networks,based on the algorithm of link rewiring of local attachment(RLA)and global attachment(RGA).Generality,the system does reach a steady state where all individuals'opinion and the complex network structure are fixed.The RGA enhances the ability of consensus of opinion formation.Furthermore,by tuning a model parameter p,which governs the proportion of RLA and RGA,we find the formation of hierarchical structure in the social networks for p>p_(c).Here,p_(c) is related to the complex network size N and the minimal coordination number 2K.The model also reproduces many features of large social networks,including the“weak links”property.
基金supported by the National Natural Science Foundation of China (10647125, 10635020, 10975057 and 10975062)the Program of Introducing Talents of Discipline to Universities (B08033)
文摘Spatial distance has a remarkable effect on the attended mode of a network embedded in a certain space. First, we investigate how spatial restriction leads to information-information correlation that is strong, linear and positive in real networks. We then construct a two-dimensional space, define the action radius R for nodes of networks, and propose a class of models that depend on spatial distance. Information correlation of the models is consistent with that of real networks. The spatial distance plays a leading role in generating assortative mixing by degree, while the generation of disassortative mixing relies on both the degree of preferential attachment and spatial restriction.
基金supported in part by the National Natural Science Foundation of China (10647125, 10635020, 10975057, 10975062)the Programme of Introducing Tal-ents of Discipline to Universities (B08033)
文摘Motivated by the need to include the different characteristics of individuals and the damping effect in predictions of epidemic spreading, we build a model with variant coefficients and white Gaussian noise based on the traditional SIR model. The analytic and simulation results predicted by the model are presented and discussed. The simulations show that using the variant coefficients results in a higher percentage of susceptible individuals and a lower percentage of removed individuals. When the noise is included in the model, the percentage of infected individuals has a wider peak and more fluctuations than that predicted using the traditional SIR model.
基金supported by the Chinese Ministry of Education (2008677010)the National Natural Science Foundation of China (10647125, 10635020, 10975057, 10975062)the Programme of Introducing Talents of Discipline to Universities (B08033)
文摘Varentropy is used as a general measure of probabilistic uncertainty for a complex network, inspired by the first and second laws of thermodynamics, but not limited to the equilibrium system. By exploring the relationship between the varentropy of the scale free distribution and the exponent of power laws as well as network size, we get the optimal design of a scale-free network against random failures. The behaviors of varentropy and the Shannon entropy of double Pareto law degree distribution are analyzed to compare their usefulness. Our conclusion is that varentropy is suitable and reliable.