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1.
Many social, technological, biological and economical systems are properly described by evolved network models. In this paper, a new evolving network model with the concept of physical position neighbourhood connectivity is proposed and studied. This concept exists in many real complex networks such as communication networks. The simulation results for network parameters such as the first nonzero eigenvalue and maximal eigenvalue of the graph Laplacian, clustering coefficients, average distances and degree distributions for different evolving parameters of this model are presented. The dynamical behaviour of each node on the consensus problem is also studied. It is found that the degree distribution of this new model represents a transition between power-law and exponential scaling, while the Barábasi-Albert scale-free model is only one of its special (limiting) cases. It is also found that the time to reach a consensus becomes shorter sharply with increasing of neighbourhood scale of the nodes. 相似文献
2.
Aimed at lowering the effect of `rich get richer' in scale-free
networks with the Barab\'{a}si and Albert model, this paper
proposes a new evolving mechanism, which
includes dividing and preference attachment for the growth of a
network. A broad scale characteristic which is independent of the
initial network topology is obtained with the proposed model. By
simulating, it is found that preferential attachment causes the
appearance of the scale-free characteristic,
while the dividing will decrease the power-law behaviour and
drive the evolution of broad scale networks. 相似文献
3.
Scale-free networks are characterized by a degree distribution with power-law behavior. Although scale-free networks have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks, degree distributions of other observed networks often differ from the power-law type. Data based investigations require modifications of the typical scale-free network.We present an algorithm that generates networks in which the shape of the degree distribution is tunable by modifying the preferential attachment step of the Barabási-Albert construction algorithm. The shape of the distribution is represented by dispersion measures such as the variance and the skewness, both of which are highly correlated with the maximal degree of the network and, therefore, adequately represents the influence of superspreaders or hubs. By combining our algorithm with work of Holme and Kim, we show how to generate networks with a variety of degree distributions and clustering coefficients. 相似文献
4.
5.
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
6.
We discuss merging-and-creation as a self-organizing process for scale-free topologies in networks. Three power-law classes characterized by the power-law exponents
, 2 and
are identified and the process is generalized to networks. In the network context the merging can be viewed as a consequence of optimization related to more efficient signaling. 相似文献
7.
针对真实世界中大规模网络都具有明显聚类效应的特点, 提出一类具有高聚类系数的加权无标度网络演化模型, 该模型同时考虑了优先连接、三角结构、随机连接和社团结构等四种演化机制. 在模型演化规则中, 以概率p增加单个节点, 以概率1–p增加一个社团. 与以往研究的不同在于新边的建立, 以概率φ在旧节点之间进行三角连接, 以概率1–φ进行随机连接. 仿真分析表明, 所提出的网络度、强度和权值分布都是服从幂律分布的形式, 且具有高聚类系数的特性, 聚类系数的提高与社团结构和随机连接机制有直接的关系. 最后通过数值仿真分析了网络演化机制对同步动态特性的影响, 数值仿真结果表明, 网络的平均聚类系数越小, 网络的同步能力越强.
关键词:
无标度网络
加权网络
聚类系数
同步能力 相似文献
8.
This paper studies and predicts the number growth of China's mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, in which the nodes grow following a power-law acceleration. The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process. This result shows that the model generates appropriate power-law connectivity distributions. Therefore, we find a power-law acceleration invariance of the scale-free networks. The numerical simulations of the models agree with the analytical results well. 相似文献
9.
We analyze the correlation properties of the Erdos-Rényi random graph (RG) and the Barabási-Albert scale-free network (SF) under the attack and repair strategy with detrended fluctuation analysis (DFA). The maximum degree k representing the local property of the system, shows similar scaling behaviors for random graphs and scale-free networks. The fluctuations are quite random at short time scales but display strong anticorrelation at longer time scales under the same system size N and different repair probability pre. The average degree , revealing the statistical property of the system, exhibits completely different scaling behaviors for random graphs and scale-free networks. Random graphs display long-range power-law correlations. Scale-free networks are uncorrelated at short time scales; while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of pre. 相似文献
10.
In this paper, we proposed an ungrowing scale-free network model, indicating the growth may not be a necessary condition of the self-organization of a network in a scale-free structure. The analysis shows that the degree distributions of the present model can varying from the Poisson form to the power-law form with the decrease of a free parameter α. This model provides a possible mechanism for the evolution of some scale-free networks with fixed size, such as the friendship networks of school children and the functional networks of the human brain. 相似文献
11.
To study transport properties of scale-free and Erdos-Rényi networks, we analyze the conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)-k(-lambda) in which all links have unit resistance. We predict a broad range of values of G, with a power-law tail distribution phi(SF)(G)-G(-g(G)), where g(G)=2lambda-1, and confirm our predictions by simulations. The power-law tail in phi(SF)(G) leads to large values of G, signaling better transport in scale-free networks compared to Erdos-Rényi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical "transport backbone" picture we show that the conductances of scale-free and Erdos-Rényi networks are well approximated by ck(A)k(B)/(k(A)+k(B)) for any pair of nodes A and B with degrees k(A) and k(B), where c emerges as the main parameter characterizing network transport. 相似文献
12.
13.
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
14.
A universal estimation formula for the average path length of scale
free networks is given in this paper. Different from other
estimation formulas, most of which use the size of network, $N$, as
the only parameter, two parameters including $N$ and a second
parameter $\alpha $ are included in our formula. The parameter
$\alpha $ is the power-law exponent, which represents the local
connectivity property of a network. Because of this, the formula
captures an important property that the local connectivity property
at a microscopic level can determine the global connectivity of the
whole network. The use of this new parameter distinguishes this
approach from the other estimation formulas, and makes it a
universal estimation formula, which can be applied to all types of
scale-free networks. The conclusion is made that the small world
feature is a derivative feature of a scale free network. If a
network follows the power-law degree distribution, it must be a
small world network. The power-law degree distribution property,
while making the network economical, preserves the efficiency
through this small world property when the network is scaled up. In
other words, a real scale-free network is scaled at a relatively
small cost and a relatively high efficiency, and that is the
desirable result of self-organization optimization. 相似文献
15.
Zhongzhi Zhang Shuigeng Zhou Lichao Chen Jihong Guan Lujun Fang Yichao Zhang 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,59(1):99-107
We propose a geometric growth model for weighted
scale-free networks, which is controlled by two tunable parameters.
We derive exactly the main characteristics of the networks, which
are partially determined by the parameters. Analytical results
indicate that the resulting networks have power-law distributions of
degree, strength, weight and betweenness, a scale-free behavior for
degree correlations, logarithmic small average path length and
diameter with network size. The obtained properties are in agreement
with empirical data observed in many real-life networks, which shows
that the presented model may provide valuable insight into the real
systems. 相似文献
16.
S. Carmi Z. Wu E. López S. Havlin H. Eugene Stanley 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(2):165-174
We study the transport properties of model networks such as
scale-free and Erd?s-Rényi networks as well as a real
network. We consider few possibilities for the trnasport problem.
We start by studying the conductance G between two arbitrarily
chosen nodes where each link has the same unit resistance. Our
theoretical analysis for scale-free networks predicts a broad
range of values of G, with a power-law tail distribution
$\Phi_{\rm SF}(G)\sim G^{-g_G}$
, where gG=2λ-1, and
λ is the decay exponent for the scale-free network degree
distribution. The power-law tail in ΦSF(G) leads to
large values of G, thereby significantly improving the transport
in scale-free networks, compared to Erd?s-Rényi networks
where the tail of the conductivity distribution decays
exponentially. We develop a simple physical picture of the
transport to account for the results. The other model for
transport is the max-flow model, where conductance is defined
as the number of link-independent paths between the two nodes, and
find that a similar picture holds. The effects of distance on the
value of conductance are considered for both models, and some
differences emerge. We then extend our study to the case of
multiple sources ans sinks, where the transport is defined between two
groups of nodes. We find a fundamental difference between
the two forms of flow when considering the quality of the
transport with respect to the number of sources, and find an
optimal number of sources, or users, for the max-flow case. A
qualitative (and partially quantitative) explanation is also
given. 相似文献
17.
The explicit determination of the number of monomer-dimer arrangements on a network is a theoretical challenge, and exact solutions to monomer-dimer problem are available only for few limiting graphs with a single monomer on the boundary, e.g., rectangular lattice and quartic lattice; however, analytical research (even numerical result) for monomer-dimer problem on scale-free small-world networks is still missing despite the fact that a vast variety of real systems display simultaneously scale-free and small-world structures. In this paper, we address the monomer-dimer problem defined on a scale-free small-world network and obtain the exact formula for the number of all possible monomer-dimer arrangements on the network, based on which we also determine the asymptotic growth constant of the number of monomer-dimer arrangements in the network. We show that the obtained asymptotic growth constant is much less than its counterparts corresponding to two-dimensional lattice and Sierpinski fractal having the same average degree as the studied network, which indicates from another aspect that scale-free networks have a fundamentally distinct architecture as opposed to regular lattices and fractals without power-law behavior. 相似文献
18.
《Physics letters. A》2006,349(6):462-466
Many social, technological, biological and economical systems are best described by evolved network models. In this short Letter, we propose and study a new evolving network model. The model is based on the new concept of neighbourhood connectivity, which exists in many physical complex networks. The statistical properties and dynamics of the proposed model is analytically studied and compared with those of Barabási–Albert scale-free model. Numerical simulations indicate that this network model yields a transition between power-law and exponential scaling, while the Barabási–Albert scale-free model is only one of its special (limiting) cases. Particularly, this model can be used to enhance the evolving mechanism of complex networks in the real world, such as some social networks development. 相似文献
19.
20.
Pinning control of scale-free dynamical networks 总被引:16,自引:0,他引:16
Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions have the power-law form. In the present work, control of a scale-free dynamical network by applying local feedback injections to a fraction of network nodes is investigated. The specifically and randomly pinning schemes are considered. The specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme. The method is applied to an array of Chua's oscillators as an example. 相似文献