共查询到20条相似文献,搜索用时 31 毫秒
1.
We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in nongrowth random networks.In this model,we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it.The network evolves according to a vertex strength preferential selection mechanism.During the evolution process,the network always holds its total number of vertices and its total number of single-edges constantly.We show analytically and numerically that a network will form steady scale-free distributions with our model.The results show that a weighted non-growth random network can evolve into scale-free state.It is interesting that the network also obtains the character of an exponential edge weight distribution.Namely,coexistence of scale-free distribution and exponential distribution emerges. 相似文献
2.
Inspired by scientific collaboration networks (SCN), especially our empirical analysis of econophysicists network, an evolutionary model for weighted networks is proposed. Besides a new vertex added in at every time step, old vertices can also attempt to build up new links, or to reconnect the existing links. The number of connections repeated between two nodes is converted into the weight of the link. This provides a natural way for the evolution of link weight. The path-dependent preferential attachment mechanism with local information is also introduced. It increases the clustering coefficient of the network significantly. The model shows the scale-free phenomena in degree and vertex weight distribution. It also gives well qualitatively consistent behavior with the empirical results. 相似文献
3.
Scale-Free Graph with Preferential Attachment and Evolving Internal Vertex Structure 总被引:1,自引:0,他引:1
Krzysztof Choromański Michał Matuszak Jacek Miȩkisz 《Journal of statistical physics》2013,151(6):1175-1183
We extend the classical Barabási-Albert preferential attachment procedure to graphs with internal vertex structure given by weights of vertices. In our model, weight dynamics depends on the current vertex degree distribution and the preferential attachment procedure takes into account both weights and degrees of vertices. We prove that such a coupled dynamics leads to scale-free graphs with exponents depending on parameters of the weight dynamics. 相似文献
4.
Effects of vertex activity have been analyzed on a weighted
evolving network. The network is characterized by the probability
distribution of vertex strength, each edge weight and evolution of
the strength of vertices with different vertex activities. The model exhibits self-organized criticality behavior. The
probability distribution of avalanche size for different network sizes is also shown. In addition, there is a power law relation between the size and the duration of an avalanche and the average of avalanche size has been studied for different vertex activities. 相似文献
5.
We present the network of scientific journals pertaining to Chinese patent data in the period of 1995-2002, in which two journals are considered linked if they have been cited by a common patent. We study a variety of statistical properties of the network of scientific journals of China (NSJC), including degree distribution, local clustering and average degree of the nearest neighbors in the one-mode projected network. Besides this, we generate a weighted network for the NSJC in which the number of common patents citing two particular journals is mapped to line weights. For such a weighted network, distributions of weight, vertex strength, weight per degree, and the relationship between the vertex strength and degree have been analyzed. The above findings show that for the NSJC, small-world behavior is not distinct, while properties of random networks are observed. 相似文献
6.
We propose a weighted clique network evolution model, which expands continuously by the addition of a new clique (maximal complete sub-graph) at each time step. And the cliques in the network overlap with each other. The structural expansion of the weighted clique network is combined with the edges' weight and vertices' strengths dynamical evolution. The model is based on a weight-driven dynamics and a weights' enhancement mechanism combining with the network growth. We study the network properties, which include the distribution of vertices' strength and the distribution of edges' weight, and find that both the distributions follow the scale-free distribution. At the same time, we also find that the relationship between strength and degree of a vertex are linear correlation during the growth of the network. On the basis of mean-field theory, we study the weighted network model and prove that both vertices' strength and edges' weight of this model follow the scale-free distribution. And we exploit an algorithm to forecast the network dynamics, which can be used to reckon the distributions and the corresponding scaling exponents. Furthermore, we observe that mean-field based theoretic results are
consistent with the statistical data of the model, which denotes the theoretical result in this paper is effective. 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.
The collaboration network generated by the Erasmus student mobilities in the year 2003 is analyzed and modeled. Nodes of this bipartite network are European universities and links are the Erasmus mobilities between these universities. This network is a complex directed and weighted graph. The non-directed and non-weighted projection of this network does not exhibit a scale-free nature, but proves to be a small-word type random network with a giant component. The connectivity data indicates an exponential degree distribution, a relatively high clustering coefficient and a small radius. It can be easily modeled by using a simple configuration model and arguing the exponential degree distribution. The weighted and directed version of the network can also be described by means of simple random network models. 相似文献
9.
《Nuclear Physics B》1997,491(3):689-723
We study the large-N limit of a class of matrix models for dually weighted triangulated random surfaces using character expansion techniques. We show that for various choices of the weights of vertices of the dynamical triangulation the model can be solved by resumming the Itzykson-Di Francesco formula over congruence classes of Young tableau weights modulo three. From this we show that the large-N limit implies a non-trivial correspondence with models of random surfaces weighted with only even coordination number vertices. We examine the critical behaviour and evaluation of observables and discuss their interrelationships in all models. We obtain explicit solutions of the model for simple choices of vertex weightings and use them to show how the matrix model reproduces features of the random surface sum. We also discuss some general properties of large-N character expansion approach as well as potential physical applications of our results. 相似文献
10.
Many real systems possess accelerating statistics where the total number of edges grows faster than the network size. In this paper, we propose a simple weighted network model with accelerating growth. We derive analytical expressions for the evolutions and distributions for strength, degree, and weight, which are relevant to accelerating growth. We also find that accelerating growth determines the clustering coefficient of the networks. Interestingly, the distributions for strength, degree, and weight display a transition from scale-free to exponential form when the parameter with respect to accelerating growth increases from a small to large value. All the theoretical predictions are successfully contrasted with numerical simulations. 相似文献
11.
A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently
equipped with a random number of half-edges and each half-edge is assigned an integer valued weight according to a distribution
that is allowed to depend on the degree of its vertex. Half-edges with the same weight are then paired randomly to create
edges. An expression for the threshold for the appearance of a giant component in the resulting graph is derived using results
on multi-type branching processes. The same technique also gives an expression for the basic reproduction number for an epidemic
on the graph where the probability that a certain edge is used for transmission is a function of the edge weight (reflecting
how closely ‘connected’ the corresponding vertices are). It is demonstrated that, if vertices with large degree tend to have
large (small) weights on their edges and if the transmission probability increases with the edge weight, then it is easier
(harder) for the epidemic to take off compared to a randomized epidemic with the same degree and weight distribution. A recipe
for calculating the probability of a large outbreak in the epidemic and the size of such an outbreak is also given. Finally,
the model is fitted to three empirical weighted networks of importance for the spread of contagious diseases and it is shown
that R
0 can be substantially over- or underestimated if the correlation between degree and weight is not taken into account. 相似文献
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13.
We present a weighted scale-free network model, in which the power-law exponents can be controlled by the model parameters. The network is generated through the weight-driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links. The simplicity of the model enables us to derive analytically the various statistical properties, such as the distributions of degree, strength, and weight, the degree-strength and degree-weight relationship, and the dependencies of these power-law exponents on the model parameters. Finally, we demonstrate that networks of words, coauthorship of researchers, and collaboration of actor/actresses are quantitatively well described by this model. 相似文献
14.
In this paper, we analyze an evolving model with local information which can generate a class of networks by choosing different values of the parameter p. The model introduced exhibits the transition from unweighted networks to weighted networks because the distribution of the edge weight can be widely tuned. With the increase in the local information, the degree correlation of the network transforms from assortative to disassortative. We also study the distribution of the degree, strength and edge weight, which all show crossover between exponential and scale-free. Finally, an application of the proposed model to the study of the synchronization is considered. It is concluded that the synchronizability is enhanced when the heterogeneity of the edge weight is reduced. 相似文献
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D.-H. Kim B. Kahng D. Kim 《The European Physical Journal B - Condensed Matter and Complex Systems》2004,38(2):305-309
The static model was introduced to generate a scale-free network. In the model, N number of vertices are present from the beginning. Each vertex has its own weight, representing how much the vertex is influential in a system. The static model, however, is not relevant, when a complex network is composed of many modules such as communities in social networks. An individual may belong to more than one community and has distinct weights for each community. Thus, we generalize the static model by assigning a q-component weight on each vertex. We first choose a component
among the q components at random and a pair of vertices is linked with a color according to their weights of the component
as in the static model. A (1-f) fraction of the entire edges is connected following this way. The remaining fraction f is added with (q + 1)-th color as in the static model but using the maximum weights among the q components each individual has. The social activity with such maximum weights is an essential ingredient to enhance the assortativity coefficient as large as the ones of real social networks.Received: 27 October 2003, Published online: 17 February 2004PACS:
89.65.-s Social and economic systems - 89.75.Hc Networks and genealogical trees - 89.75.Da Systems obeying scaling laws 相似文献
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加权网络可以对复杂系统的相互作用结构提供更加细致的刻画,而改变边权也成为调整和改善网络性质与功能的新途径.基于已有无权网络的效率概念,文中给出了相似权和相异权网络的网络效率定义,并研究了权重分布对于网络效率的影响.从平权的规则网络出发,通过改变权重的分布形式考察权重分布对网络效率的影响,结果发现,在规则网络上,权重分布随机性的增加提高了网络效率,而在几种常见的权重分布形式中,指数分布对网络效率的改进最为显著.同时,权重随机化之后网络最小生成树的总权重减小,意味着网络的运输成本随着权重异质性的增加而降低.以上结果为深入理解权重对网络结构与功能的影响提供了基础.
关键词:
复杂网络
加权网络
权重
网络效率 相似文献