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1.
In this paper we present weighted Koch networks based on classic Koch networks. A new method is used to determine the average receiving time (ART), whose key step is to write the sum of mean first-passage times (MFPTs) for all nodes to absorption at the trap located at a hub node as a recursive relation. We show that the ART exhibits a sublinear or linear dependence on network order. Thus, the weighted Koch networks are more efficient than classic Koch networks in receiving information. Moreover, average weighted shortest path (AWSP) is calculated. In the infinite network order limit, the AWSP depends on the scaling factor. The weighted Koch network grows unbounded but with the logarithm of the network size, while the weighted shortest paths stay bounded. 相似文献
2.
Ferdinando Mancini Evgeny Plekhanov Gerardo Sica 《The European Physical Journal B - Condensed Matter and Complex Systems》2013,86(10):1-12
In this paper, we propose a family of weighted extended Koch networks based on a class of extended Koch networks. They originate from a r-complete graph, and each node in each r-complete graph of current generation produces mr-complete graphs whose weighted edges are scaled by factor h in subsequent evolutionary step. We study the structural properties of these networks and random walks on them. In more detail, we calculate exactly the average weighted shortest path length (AWSP), average receiving time (ART) and average sending time (AST). Besides, the technique of resistor network is employed to uncover the relationship between ART and AST on networks with unit weight. In the infinite network order limit, the average weighted shortest path lengths stay bounded with growing network order (0 < h < 1). The closed form expression of ART shows that it exhibits a sub-linear dependence (0 < h < 1) or linear dependence (h = 1) on network order. On the contrary, the AST behaves super-linearly with the network order. Collectively, all the obtained results show that the efficiency of message transportation on weighted extended Koch networks has close relation to the network parameters h, m and r. All these findings could shed light on the structure and random walks of general weighted networks. 相似文献
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Many social and biological networks consist of communities–groups of nodes within which links are dense but among which links are sparse. It turns out that most of these networks are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the link weights among their nodes. Recently, there are considerable interests in the study of properties as well as modelling of such networks with community structures. To our knowledge, however, no study of any weighted network model with such a community structure has been presented in the literature to date. In this paper, we propose a weighted evolving network model with a community structure. The new network model is based on the inner-community and inter-community preferential attachments and preferential strengthening mechanism. Simulation results indicate that this network model indeed reflect the intrinsic community structure, with various power-law distributions of the node degrees, link weights, and node strengths. 相似文献
5.
Many real-world systems can be modeled by weighted small-world networks with high clustering coefficients. Recent studies for rigorously analyzing the weighted spectral distribution(W SD) have focused on unweighted networks with low clustering coefficients. In this paper, we rigorously analyze the W SD in a deterministic weighted scale-free small-world network model and find that the W SD grows sublinearly with increasing network order(i.e., the number of nodes) and provides a sensitive discrimination for each input of this model. This study demonstrates that the scaling feature of the W SD exists in the weighted network model which has high and order-independent clustering coefficients and reasonable power-law exponents. 相似文献
6.
k-核分解排序法对于度量复杂网络上重要节点的传播影响力具有重要的理论意义和应用价值,但其排序粗粒化的缺陷也不容忽视.最新研究发现,一些真实网络中存在局域连接稠密的特殊构型是导致上述问题的根本原因之一.当前的解决方法是利用边两端节点的外部连边数度量边的扩散性,采取过滤网络边来减少这种稠密结构给k-核分解过程造成的干扰,但这种方法并没有考虑现实网络上存在权重的普遍性.本文利用节点权重和权重分布重新定义边的扩散性,提出适用于加权网络结构的基于冗余边过滤的k-核分解排序算法:filter-core.通过世界贸易网、线虫脑细胞网和科学家合著网等真实网络的SIR(susceptible-infectedrecovered)传播模型的仿真结果表明,该算法相比其他加权k-核分解法,能够更准确地度量加权网络上具有重要传播影响力的核心节点及核心层. 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.
Zhongzhi Zhang Shuyang Gao 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,80(2):209-216
Random walks on complex networks, especially scale-free
networks, have attracted considerable interest in the past few
years. A lot of previous work showed that the average receiving time
(ART), i.e., the average of mean first-passage time (MFPT) for
random walks to a given hub node (node with maximum degree) averaged
over all starting points in scale-free small-world networks exhibits
a sublinear or linear dependence on network order N (number of
nodes), which indicates that hub nodes are very efficient in
receiving information if one looks upon the random walker as an
information messenger. Thus far, the efficiency of a hub node
sending information on scale-free small-world networks has not been
addressed yet. In this paper, we study random walks on the class of
Koch networks with scale-free behavior and small-world effect. We
derive some basic properties for random walks on the Koch network
family, based on which we calculate analytically the average sending
time (AST) defined as the average of MFPTs from a hub node to all
other nodes, excluding the hub itself. The obtained closed-form
expression displays that in large networks the AST grows with
network order as N ln N, which is larger than the linear scaling
of ART to the hub from other nodes. On the other hand, we also
address the case with the information sender distributed uniformly
among the Koch networks, and derive analytically the global mean
first-passage time, namely, the average of MFPTs between all couples
of nodes, the leading scaling of which is identical to that of AST.
From the obtained results, we present that although hub nodes are
more efficient for receiving information than other nodes, they
display a qualitatively similar speed for sending information as
non-hub nodes. Moreover, we show that that AST from a starting point
(sender) to all possible targets is not sensitively affected by the
sender’s location. The present findings are helpful for better
understanding random walks performed on scale-free small-world
networks. 相似文献
9.
In this paper, we present trapping issues of weight-dependent walks on weighted hierarchical networks which are based on the classic scale-free hierarchical networks. Assuming that edge’s weight is used as local information by a random walker, we introduce a biased walk. The biased walk is that a walker, at each step, chooses one of its neighbours with a probability proportional to the weight of the edge. We focus on a particular case with the immobile trap positioned at the hub node which has the largest degree in the weighted hierarchical networks. Using a method based on generating functions, we determine explicitly the mean first-passage time (MFPT) for the trapping issue. Let parameter a (0 < a < 1) be the weight factor. We show that the efficiency of the trapping process depends on the parameter a; the smaller the value of a, the more efficient is the trapping process. 相似文献
10.
V. Zlatic G. Bianconi A. Díaz-Guilera D. Garlaschelli F. Rao G. Caldarelli 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,67(3):271-275
For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made
on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a real-world
network it is therefore crucial to compare the measured results with a null model counterpart. Here we focus on dense and
weighted networks, proposing a suitable null model and studying the behaviour of the degree correlations as measured by the
rich-club coefficient. Our method solves an existing problem with the randomization of dense unweighted graphs, and at the
same time represents a generalization of the rich-club coefficient to weighted networks which is complementary to other recently
proposed ones. 相似文献
11.
We propose a deterministic weighted scale-free small-world model for considering pseudofractal web with the co-evolution of topology and weight. Considering the fluctuations in traffic flow constitute a main reason for congestion of packet delivery and poor performance of communication networks, we suggest a recursive algorithm to generate the network, which restricts the traffic fluctuations on it effectively during the evolutionary process. We provide a relatively complete view of topological structure and weight dynamics characteristics of the networks such as weight and strength distribution, degree correlations, average clustering coefficient and degree-cluster correlations as well as the diameter. 相似文献
12.
L. Tian D.-N. Shi 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(2):167-171
In this paper, we study a rank-based model for weighted network. The evolution rule of the network is based on the ranking
of node strength, which couples the topological growth and the weight dynamics. Analytically and by simulations, we demonstrate
that the generated networks recover the scale-free distributions of degree and strength in the whole region of the growth
dynamics parameter (α>0). Moreover, this network evolution mechanism can also produce scale-free property of weight, which
adds deeper comprehension of the networks growth in the presence of incomplete information. We also characterize the clustering
and correlation properties of this class of networks. It is showed that at α=1 a structural phase transition occurs, and for
α>1 the generated network simultaneously exhibits hierarchical organization and disassortative degree correlation, which is
consistent with a wide range of biological networks. 相似文献
13.
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
14.
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of a few parameters. 相似文献
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在Barrat, Barthélemy 和 Vespignani (BBV)加权无标度网络模型的基础上,提出了一种可大范围调节聚类系数的加权无标度网络模型——广义BBV模型(GBBV模型).理论分析和仿真实验表明,GBBV模型保留了BBV模型的许多特征,节点度、节点权重和边权值等都服从幂律分布.但是,GBBV模型克服了BBV模型只能小范围调节聚类系数的缺陷,从而可以用于具有大聚类系数网络的建模.
关键词:
无标度网络
加权网络
聚类系数 相似文献
17.
Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap 下载免费PDF全文
In this paper,we study the scaling for the mean first-passage time(MFPT) of the random walks on a generalized Koch network with a trap.Through the network construction,where the initial state is transformed from a triangle to a polygon,we obtain the exact scaling for the MFPT.We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order.In addition,we determine the exponents of scaling efficiency characterizing the random walks.Our results are the generalizations of those derived for the Koch network,which shed light on the analysis of random walks over various fractal networks. 相似文献
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Mei-Feng Dai Ting-Ting Ju Yong-Bo Hou Fang Huang Dong-Lei Tang Wei-Yi Su 《理论物理通讯》2020,72(5):55602-112
The weighted self-similar network is introduced in an iterative way. In order to understand the topological properties of the self-similar network, we have done a lot of research in this field.Firstly, according to the symmetry feature of the self-similar network, we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix.Then, we obtain eigenvalues of the Laplacian matrix from these two successive generations.Finally, we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix. 相似文献
20.
Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap 下载免费PDF全文
In this paper, we study the scaling for the mean first-passage time (MFPT) of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from a triangle to a polygon, we obtain the exact scaling for the MFPT. We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order. In addition, we determine the exponents of scaling efficiency characterizing the random walks. Our results are the generalizations of those derived for the Koch network, which shed light on the analysis of random walks over various fractal networks. 相似文献