Response of scale-free networks with community structure to external stimuli

The response of scale-free networks with community structure to external stimuli is studied. By disturbing some nodes with different strategies, it is shown that the robustness of this kind of network can be enhanced due to the existence of communities in the networks. Some of the response patterns are found to coincide with topological communities. We show that such phenomena also occur in the cat brain network which is an example of a scale-free like network with community structure. Our results provide insights into the relationship between network topology and the functional organization in complex networks from another viewpoint.     

Stochastic resonance in hybrid scale-free neuronal networks

We study the phenomenon of stochastic resonance in a system of coupled neurons that are globally excited by a weak periodic input signal. We make the realistic assumption that the chemical and electrical synapses interact in the same neuronal network, hence constituting a hybrid network. By considering a hybrid coupling scheme embedded in the scale-free topology, we show that the electrical synapses are more efficient than chemical synapses in promoting the best correlation between the weak input signal and the response of the system. We also demonstrate that the average degree of neurons within the hybrid scale-free network significantly influences the optimal amount of noise for the occurrence of stochastic resonance, indicating that there also exists an optimal topology for the amplification of the response to the weak input signal. Lastly, we verify that the presented results are robust to variations of the system size.     

Weighted Scaling in Non-growth Random Networks

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.     

有倾向性重连产生的反匹配网络

在具有网络结构的系统中度关联属性对于动力学行为具有重要的影响, 所以产生适当度关联网络的方法对于大量网络系统的研究具有重要的作用. 尽管产生正匹配网络的方法已经得到很好的验证, 但是产生反匹配网络的方法还没有被系统的讨论过. 重新连接网络中的边是产生度关联网络的一个常用方法. 这里我们研究使用重连方法产生反匹配无标度网络的有效性. 我们的研究表明, 有倾向的重连可以增强网络的反匹配属性. 但是有倾向重连不能使皮尔森度相关系数下降到-1, 而是存在一个依赖于网络参数的最小值. 我们研究了网络的主要参数对于网络度相关系数的影响, 包括网络尺寸, 网络的连接密度和网络节点的度差异程度. 研究表明在网络尺寸大的情况下和节点度差异性强的情况下, 重连的效果较差. 我们研究了真实Internet网络, 发现模型产生的网络经过重连不能达到真实网络的度关联系数.     

Weighted Scaling in Non-growth Random Networks

We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in non-growth 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.     

Monomer-dimer model on a scale-free small-world network

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.     

面向成本-收益好的无标度耦合网络构建方法

较大平均路径长度的网络会带来较大的网络延迟, 难以支持时间敏感业务与应用. 通过增加连接可以降低源和目的节点之间的跳数, 进而降低网络平均延迟, 使得更加快速地传播信息, 但是增加连接的同时也增加了网络构建成本. 分层网络是研究网络耦合的一个有效方法, 但目前网络构建过程中将每层网络分别处理并认为每层网络之间没有强相关性. 本文提出了一种面向成本-收益的无标度网络动态构建方法. 此方法将网络分为多层, 基于连续论在高层网络中添加连接, 使得网络演化为无标度网络. 此连续过程包括节点度增加过程和局部网络半径增长两个连续过程, 在增加连接的过程中引入表征网络构建成本和收益的成本-收益指标. 模拟结果表明引入成本-收益指标的无标度耦合网络构建方法能够在合理范围内有效降低网络平均路径长度, 提升网络性能, 并且本文给出了耦合网络的动态业务性能, 通过调整高层网络避免网络拥塞.     

一类高聚类系数的加权无标度网络及其同步能力分析

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     

Enhancement of scale-free network attack tolerance

Despite the large size of most communication and transportation systems,there are short paths between nodes in these networks which guarantee the efficient information,data and passenger delivery;furthermore these networks have a surprising tolerance under random errors thanks to their inherent scale-free topology.However,their scale-free topology also makes them fragile under intentional attacks,leaving us a challenge on how to improve the network robustness against intentional attacks without losing their strong tolerance under random errors and high message and passenger delivering capacity.Here we propose two methods (SL method and SH method) to enhance scale-free network’s tolerance under attack in different conditions.     

Information diffusion on adaptive network

Based on the adaptive network, the feedback mechanism and interplay between the network topology and the diffusive process of information are studied. The results reveal that the adaptation of network topology can drive systems into the scale-free one with the assortative or disassortative degree correlations, and the hierarchical clustering. Meanwhile, the processes of the information diffusion are extremely speeded up by the adaptive changes of network topology.     

Amplified signal response in scale-free networks by collaborative signaling

Many natural and artificial two-states signaling devices are connected forming networks. The information-processing potential of these systems is usually related to the response to weak external signals. Here, using a network of overdamped bistable elements, we study the effect of a heterogeneous complex topology on the signal response. The analysis of the problem in random scale-free networks, reveals that heterogeneity plays a crucial role in amplifying external signals. We have contrasted numerical simulations with analytical calculations in simplified topologies.     

Emergency response to disaster-struck scale-free network with redundant systems

Disasters cause tremendous damage every year. In this paper, we have specifically studied emergency response to disaster-struck scale-free networks when some nodes in the network have redundant systems. If one node collapses, its redundant system will substitute it to work for a period of time. In the first part, according to the network structure, several redundant strategies have been formulated, and then our studies focused on their effectiveness by means of simulation. Results show that the strategy based on total degrees is the most effective one. However, many nodes still collapse in the end if redundant systems do not have sufficient capability, so emergency responses are necessary. Several emergent strategies controlling the distribution of external resources have been proposed in the second part. The effectiveness of those emergent strategies are then studied from three aspects, such as the effect of strategies on spreading processes, minimum sufficient quantities of external resources and determination of the most appropriate emergent strategy. In addition, the effects of redundant intensity on these aspects have been discussed as well.     

Synchronizability of Highly Clustered Scale-Free Networks

We consider the effect of clustering coefficient on the synchronizability of coupled oscillators located on scale-free networks. The analytic result for the value of clustering coefficient aiming at a highly clustered scale-free network model, the Holme-Kim model is obtained, and the relationship between network synchronizability and clustering coefficient is reported. The simulation results strongly suggest that the more clustered the network, the poorer the synchronizability.     

增长及非增长无标度网络的成因解析

分析两类无标度网络的形成原因,提出一个无标度网络演化模型并进行一系列数值实验.基于分析和实验得到推论:只要保持足够低的网络密度,通过基于度的偏好连接就可形成长期稳定的无标度网络.规模增长和点边增删既是客观存在,又起到了控制网络密度的作用,足够低的网络密度和基于度的偏好连接是所有无标度网络共同的必要条件.推论可同时解释增长和非增长无标度网络的形成原因.研究结果有助于理解各种真实无标度网络和建立相应的模型.     

On topological properties of the octahedral Koch network

In this article, we propose an octahedral Koch network exhibiting abundant new properties compared to the triangular Koch network. Analytical expressions for the degree distribution, clustering coefficient, and average path length are presented. The scale-free feature and small-world property of the octahedral Koch network are obtained via numerical analysis. Furthermore, we show that the octahedral Koch network is assortative. Finally, we show that the projection of the octahedral Koch network on the plane is the nearest neighbor coupled Koch network, and the critical exponents of degree distribution in the octahedral Koch network is greater than three.     

小世界网络与无标度网络的社区结构研究

模块性(modularity)是度量网络社区结构(community structure)的主要参数.探讨了Watts和Strogatz的小世界网络(简称W-S模型)以及Barabàsi 等的B-A无标度网络(简称B-A模型)两类典型复杂网络模块性特点.结果显示，网络模块性受到网络连接稀疏的影响，W-S模型具有显著的社区结构，而B-A模型的社区结构特征不明显.因此，应用中应该分别讨论网络的小世界现象和无标度特性.社区结构不同于小世界现象和无标度特性，并可以利用模块性区别网络类型，因此网络复杂性指标应该包括 关键词： 模块性 社区结构 小世界网络 无标度网络     

Recursive weighted treelike networks

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.     

Correlations and clustering in a scale-free network in Euclidean space

Empirical study shows that many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. Quite often they are modular in nature also, implying occurrences of several small tightly linked groups which are connected in a hierarchical manner among themselves. Recently, we have introduced a model of spatial scale-free network where nodes pop-up at randomly located positions in the Euclidean space and are connected to one end of the nearest link of the existing network. It has been already argued that the large scale behaviour of this network is like the Barabási-Albert model. In the present paper we briefly review these results as well as present additional results on the study of non-trivial correlations present in this model which are found to have similar behaviours as in the real-world networks. Moreover, this model naturally possesses the hierarchical characteristics lacked by most of the models of the scale-free networks.      

Robustness measurement of scale-free networks based on motif entropy

As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structural integrity, functional integrity and dynamics of the networks. In order to overcome the shortcomings in the existing work on the robustness of complex networks, only nodes or edges are considered, while the defects of high-order structure in the network are ignored. From the perspective of network motif, we propose an entropy of node degree distribution based on motif to measure the robustness of scale-free networks under random attacks. The effectiveness and superiority of our method are verified and analyzed in the BA scale-free networks.     

Modelling one-dimensional driven diffusive systems by the Zero-Range Process

In order to characterize networks in the scale-free network class we study the frequency of cycles of length h that indicate the ordering of network structure and the multiplicity of paths connecting two nodes. In particular we focus on the scaling of the number of cycles with the system size in off-equilibrium scale-free networks. We observe that each off-equilibrium network model is characterized by a particular scaling in general not equal to the scaling found in equilibrium scale-free networks. We claim that this anomalous scaling can occur in real systems and we report the case of the Internet at the Autonomous System Level.Received: 15 January 2004, Published online: 14 May 2004PACS: 89.75.-k Complex systems - 89.75.Hc Networks and genealogical trees