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1.
A model, introduced earlier for the dynamics of a
generic efficiency measure in a population of agents by Majumdar
and Krapivsky (Phys. Rev. E 63, 054101 (2001)), is investigated on
scale-free networks whose degree distribution follows a power law
with the tunable exponent γ. The model shows a
delocalization transition from a stagnant phase to a growing one
when decreasing the degree exponent γ of scale-free
networks. By taking into account the specific dynamical properties
of the model and the geometrical properties of scale-free
networks, we predict the appearance of this critical transition.
This work is useful for understanding these kinds of transitions
occurring in many dynamical processes on scale-free networks. 相似文献
2.
In complex systems, responses to small perturbations are too diverse to definitely predict how much they would be, and then such diverse responses can be predicted in a probabilistic way. Here we study such a problem in scale-free networks, for example, the diameter changes by the deletion of a single vertex for various in silico and real-world scale-free networks. We find that the diameter changes are indeed diverse and their distribution exhibits an algebraic decay with an exponent zeta asymptotically. Interestingly, the exponent zeta is robust as zeta approximately 2.2(1) for most scale-free networks and insensitive to the degree exponents gamma as long as 2相似文献
3.
4.
In order to explore further the underlying mechanism of scale-free networks, we study stochastic secession as a mechanism for the creation of complex networks. In this evolution the network growth incorporates the addition of new nodes, the addition of new links between existing nodes, the deleting and rewiring of some existing links, and the stochastic secession of nodes. To random growing networks with preferential attachment, the model yields scale-free behavior for the degree distribution. Furthermore, we obtain an analytical expression of the power-law degree distribution with scaling exponent γ ranging from 1.1 to 9. The analytical expressions are in good agreement with the numerical simulation results. 相似文献
5.
Both the degree distribution and the degree-rank distribution, which is a relationship function between the degree and the rank of a vertex in the degree sequence obtained from sorting all vertices in decreasing order of degree, are important statistical properties to characterize complex networks. We derive an exact mathematical relationship between degree-rank distributions and degree distributions of complex networks. That is, for arbitrary complex networks, the degree-rank distribution can be derived from the degree distribution, and the reverse is true. Using the mathematical relationship, we study the degree-rank distributions of scale-free networks and exponential networks. We demonstrate that the degree-rank distributions of scale-free networks follow a power law only if scaling exponent λ>2. We also demonstrate that the degree-rank distributions of exponential networks follow a logarithmic law. The simulation results in the BA model and the exponential BA model verify our results. 相似文献
6.
Theory of rumour spreading in complex social networks 总被引:1,自引:0,他引:1
We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular, those mediated by the Internet). We use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks: random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumour spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumour, however, depends on the interplay between network topology and the rumour spreading rate. Our results show that scale-free social networks are prone to the spreading of rumours, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale information dissemination algorithms on the Internet. 相似文献
7.
This paper theoretically and empirically studies the degree and connectivity of the Internet's scale-free topology at an autonomous system (AS) level. The basic features of scale-free networks influence the normalization constant of degree distribution p(k). It develops a new mathematic model for describing the power-law relationships of Internet topology. From this model we theoretically obtain formulas to calculate the average degree, the ratios of the kmin-degree (minimum degree) nodes and the kmax-degree (maximum degree) nodes, and the fraction of the degrees (or links) in the hands of the richer (top best-connected) nodes. It finds that the average degree is larger for a smaller power-law exponent λ and a larger minimum or maximum degree. The ratio of the kmin-degree nodes is larger for larger λ and smaller kmin or kmax. The ratio of the kmax-degree ones is larger for smaller λ and kmax or larger kmin. The richer nodes hold most of the total degrees of Internet AS-level topology. In addition, it is revealed that the increased rate of the average degree or the ratio of the k_min-degree nodes has power-law decay with the increase of kmin. The ratio of the kmax-degree nodes has a power-law decay with the increase of kmax, and the fraction of the degrees in the hands of the richer 27% nodes is about 73% (the '73/27 rule'). Finally, empirically calculations are made, based on the empirical data extracted from the Border Gateway Protocol, of the average degree, ratio and fraction using this method and other methods, and find that this method is rigorous and effective for Internet AS-level topology. 相似文献
8.
由Internet构成的复杂网络的动力学特性主要受到用户需求行为的影响,具备时域的统计规律性. 通过对区域群体用户需求行为的时域实验统计分析,发现用户对Web网站的访问频度及其生成的二分网络的入度分布也呈现幂律分布和集聚现象,其幂指数介于1.7到1.8之间. 建立了虚拟资源网络VRN和物理拓扑网络PTN双层模型,分析了双层模型映射机理,并对网络用户需求行为进行建模. 虚拟资源网络VRN对物理拓扑网络PTN映射过程的不同机理,模拟了Internet资源网络到物理网络的不同影响模式. 幂律分布的用户需求特性会
关键词:
复杂网络
无标度拓扑
用户需求
相变 相似文献
9.
Large-scale genomic technologies has opened new possibilities to infer gene regulatory networks from time series data. Here, we investigate the relationship between the dynamic information of gene expression in time series and the underlying network structure. First, our results show that the distribution of gene expression fluctuations (i.e., standard deviation) follows a power-law. This finding indicates that while most genes exhibit a relatively low variation in expression level, a few genes are revealed as highly variable genes. Second, we propose a stochastic model that explains the emergence of this power-law behavior. The model derives a relationship that connects the standard deviation (variance) of each node to its degree. In particular, it allows us to identify a global property of the underlying genetic regulatory network, such as the degree exponent, by only computing dynamic information. This result not only offers an interesting link to explore the topology of real systems without knowing the real structure but also supports earlier findings showing that gene networks may follow a scale-free distribution. 相似文献
10.
11.
The evolution of Internet topology is not always smooth but sometimes with unusual sudden changes. Consequently, identifying patterns of unusual topology evolution is critical for Internet topology modeling and simulation. We analyze IPv6 Internet topology evolution in IP-level graph to demonstrate how it changes in uncommon ways to restructure the Internet. After evaluating the changes of average degree, average path length, and some other metrics over time, we find that in the case of a large-scale growing the Internet becomes more robust; whereas in a top-bottom connection enhancement the Internet maintains its efficiency with links largely decreased. 相似文献
12.
A. Korn 《Physica A》2009,388(11):2221-2226
We propose a new node centrality measure in networks, the lobby index, which is inspired by Hirsch’s h-index. It is shown that in scale-free networks with exponent α the distribution of the l-index has power tail with exponent α(α+1). Properties of the l-index and extensions are discussed. 相似文献
13.
In this work, we first formulate the Tsallis entropy in the context of complex networks. We then propose a network construction whose topology maximizes the Tsallis entropy. The growing network model has two main ingredients: copy process and random attachment mechanism (C-R model). We show that the resulting degree distribution exactly agrees with the required degree distribution that maximizes the Tsallis entropy. We also provide another example of network model using a combination of preferential and random attachment mechanisms (P-R model) and compare it with the distribution of the Tsallis entropy. In this case, we show that by adequately identifying the exponent factor q, the degree distribution can also be written in the q-exponential form. Taken together, our findings suggest that both mechanisms, copy process and preferential attachment, play a key role for the realization of networks with maximum Tsallis entropy. Finally, we discuss the interpretation of q parameter of the Tsallis entropy in the context of complex networks. 相似文献
14.
S-curve networks and an approximate method for estimating degree distributions of complex networks
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In the study of complex networks almost all theoretical models have the property of infinite growth,but the size of actual networks is finite.According to statistics from the China Internet IPv4(Internet Protocol version 4) addresses,this paper proposes a forecasting model by using S curve(logistic curve).The growing trend of IPv4 addresses in China is forecasted.There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6.Based on the laws of IPv4 growth,that is,the bulk growth and the finitely growing limit,it proposes a finite network model with a bulk growth.The model is said to be an S-curve network.Analysis demonstrates that the analytic method based on uniform distributions(i.e.,Barab’asi-Albert method) is not suitable for the network.It develops an approximate method to predict the growth dynamics of the individual nodes,and uses this to calculate analytically the degree distribution and the scaling exponents.The analytical result agrees with the simulation well,obeying an approximately power-law form.This method can overcome a shortcoming of Baraba’si-Albert method commonly used in current network research. 相似文献
15.
Unlike other natural network systems, assortativity can be observed in most human social networks, although it has been reported that a social dilemma situation represented by the prisoner’s dilemma favors dissortativity to enhance cooperation. We established a new coevolutionary model for both agents’ strategy and network topology, where teaching and learning agents coexist. Remarkably, this model enables agents’ enhancing cooperation more than a learners-only model on a time-frozen scale-free network and produces an underlying assortative network with a fair degree of power-law distribution. The model may imply how and why assortative networks are adaptive in human society. 相似文献
16.
Previous work shows that the mean first-passage time (MFPT) for random walks to a given hub node (node with maximum degree) in uncorrelated random scale-free networks is closely related to the exponent γ of power-law degree distribution P(k) ~ k(-γ), which describes the extent of heterogeneity of scale-free network structure. However, extensive empirical research indicates that real networked systems also display ubiquitous degree correlations. In this paper, we address the trapping issue on the Koch networks, which is a special random walk with one trap fixed at a hub node. The Koch networks are power-law with the characteristic exponent γ in the range between 2 and 3, they are either assortative or disassortative. We calculate exactly the MFPT that is the average of first-passage time from all other nodes to the trap. The obtained explicit solution shows that in large networks the MFPT varies lineally with node number N, which is obviously independent of γ and is sharp contrast to the scaling behavior of MFPT observed for uncorrelated random scale-free networks, where γ influences qualitatively the MFPT of trapping problem. 相似文献
17.
Through the distinction between “real” and “virtual” links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with preferential attachment, our procedure is both faster than a naïve implementation of the Barabási and Albert model and exhibits different clustering properties. The model is thoroughly studied numerically and suggests that reducing the set of partners a node can connect to is important in seizing the diversity of scale-free structures. 相似文献
18.
To study the robustness of complex networks under attack and repair, we introduce a repair model of complex networks. Based on the model, we introduce two new quantities, i.e. attack fraction fa and the maximum degree of the nodes that have never been attacked ~Ka, to study analytically the critical attack fraction and the relative size of the giant component of complex networks under attack and repair, using the method of generating function. We show analytically and numerically that the repair strategy significantly enhances the robustness of the scale-free network and the effect of robustness improvement is better for the scale-free networks with a smaller degree exponent. We discuss the application of our theory in relation to the
understanding of robustness of complex networks with reparability. 相似文献
understanding of robustness of complex networks with reparability. 相似文献
19.
Zhongzhi Zhang Shuigeng Zhou Lichao Chen 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,58(3):337-344
We present a family of scale-free network model consisting
of cliques, which is established by a simple recursive algorithm. We
investigate the networks both analytically and numerically. The
obtained analytical solutions show that the networks follow a
power-law degree distribution, with degree exponent continuously
tuned between 2 and 3. The exact expression of clustering
coefficient is also provided for the networks. Furthermore, the
investigation of the average path length reveals that the networks
possess small-world feature. Interestingly, we find that a special
case of our model can be mapped into the Yule process. 相似文献
20.
Normalized entropy of rank distribution: a novel measure of heterogeneity of complex networks 总被引:1,自引:0,他引:1
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Many unique properties of complex networks result from heterogeneity. The measure and analysis of heterogeneity are
important and desirable to the research of the properties and
functions of complex networks. In this paper, the rank distribution
is proposed as a new statistic feature of complex networks. Based on
the rank distribution, a novel measure of the heterogeneity called a
normalized entropy of rank distribution (NERD) is proposed. The NERD
accords with the normal meaning of heterogeneity within the context
of complex networks compared with conventional measures. The
heterogeneity of scale-free networks is studied using the NERD. It
is shown that scale-free networks become more heterogeneous as the
scaling exponent decreases and the NERD of scale-free networks is
independent of the number of vertices, which indicates that the NERD
is a suitable and effective measure of heterogeneity for networks
with different sizes. 相似文献