Self-similarity of complex networks

Complex networks have been studied extensively owing to their relevance to many real systems such as the world-wide web, the Internet, energy landscapes and biological and social networks. A large number of real networks are referred to as 'scale-free' because they show a power-law distribution of the number of links per node. However, it is widely believed that complex networks are not invariant or self-similar under a length-scale transformation. This conclusion originates from the 'small-world' property of these networks, which implies that the number of nodes increases exponentially with the 'diameter' of the network, rather than the power-law relation expected for a self-similar structure. Here we analyse a variety of real complex networks and find that, on the contrary, they consist of self-repeating patterns on all length scales. This result is achieved by the application of a renormalization procedure that coarse-grains the system into boxes containing nodes within a given 'size'. We identify a power-law relation between the number of boxes needed to cover the network and the size of the box, defining a finite self-similar exponent. These fundamental properties help to explain the scale-free nature of complex networks and suggest a common self-organization dynamics.     

复杂网络中的社区发现--理论与应用

复杂网络是对于复杂系统的高度抽象,其中许多性质如小世界性质、无标度性质以及聚集性质等等已经得到了充分的研究。大量文献表明,复杂网络呈现出的社区结构(Communitystructure)特性,以及如何在大型网络中高效地发现社区(Communityfinding)问题是近年来复杂网络的研究热点。本文较为全面地综述了关于社区发现方面的概念、理论、算法及应用等,期望对于社区发现问题的进一步研究及若干基本问题的早日解决起到一定作用。     

Error and attack tolerance of complex networks

Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network. Complex communication networks display a surprising degree of robustness: although key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these and other complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. Here we demonstrate that error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneously wired networks, called scale-free networks, which include the World-Wide Web, the Internet, social networks and cells. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network's connectivity). Such error tolerance and attack vulnerability are generic properties of communication networks.     

Structural Properties of Complex Networks

When complex networks describe a wide range of systems in nature and society,it is increasingly recognized that the topology of real networks are governed by robust organizing principles.Here we discuss the structural metrics such as average path length,clustering coefficient and degree distribution,the main models covering random graphs,small-world and scale-free networks,the interplay between structural properties and the synchronization of complex networks.     

Hierarchical structure and the prediction of missing links in networks

Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, in which vertices divide into groups that further subdivide into groups of groups, and so forth over multiple scales. In many cases the groups are found to correspond to known functional units, such as ecological niches in food webs, modules in biochemical networks (protein interaction networks, metabolic networks or genetic regulatory networks) or communities in social networks. Here we present a general technique for inferring hierarchical structure from network data and show that the existence of hierarchy can simultaneously explain and quantitatively reproduce many commonly observed topological properties of networks, such as right-skewed degree distributions, high clustering coefficients and short path lengths. We further show that knowledge of hierarchical structure can be used to predict missing connections in partly known networks with high accuracy, and for more general network structures than competing techniques. Taken together, our results suggest that hierarchy is a central organizing principle of complex networks, capable of offering insight into many network phenomena.     

Stability criteria for complex ecosystems

Forty years ago, May proved that sufficiently large or complex ecological networks have a probability of persisting that is close to zero, contrary to previous expectations. May analysed large networks in which species interact at random. However, in natural systems pairs of species have well-defined interactions (for example predator-prey, mutualistic or competitive). Here we extend May's results to these relationships and find remarkable differences between predator-prey interactions, which are stabilizing, and mutualistic and competitive interactions, which are destabilizing. We provide analytic stability criteria for all cases. We use the criteria to prove that, counterintuitively, the probability of stability for predator-prey networks decreases when a realistic food web structure is imposed or if there is a large preponderance of weak interactions. Similarly, stability is negatively affected by nestedness in bipartite mutualistic networks. These results are found by separating the contribution of network structure and interaction strengths to stability. Stable predator-prey networks can be arbitrarily large and complex, provided that predator-prey pairs are tightly coupled. The stability criteria are widely applicable, because they hold for any system of differential equations.     

Quantifying social group evolution

The rich set of interactions between individuals in society results in complex community structure, capturing highly connected circles of friends, families or professional cliques in a social network. Thanks to frequent changes in the activity and communication patterns of individuals, the associated social and communication network is subject to constant evolution. Our knowledge of the mechanisms governing the underlying community dynamics is limited, but is essential for a deeper understanding of the development and self-optimization of society as a whole. We have developed an algorithm based on clique percolation that allows us to investigate the time dependence of overlapping communities on a large scale, and thus uncover basic relationships characterizing community evolution. Our focus is on networks capturing the collaboration between scientists and the calls between mobile phone users. We find that large groups persist for longer if they are capable of dynamically altering their membership, suggesting that an ability to change the group composition results in better adaptability. The behaviour of small groups displays the opposite tendency-the condition for stability is that their composition remains unchanged. We also show that knowledge of the time commitment of members to a given community can be used for estimating the community's lifetime. These findings offer insight into the fundamental differences between the dynamics of small groups and large institutions.     

复杂网络的社团结构发现

社团结构是复杂网络的一个重要拓扑特征,社团结构发现是研究复杂网络的一个基础性问题,近十年来得到了广泛的关注。本文概要了非重叠社团发现的典型算法,较全面地归纳分析了重叠社团发现算法。并指出了社团发现研究尚存在的一些问题和进一步的研究方向。     

Weak pairwise correlations imply strongly correlated network states in a neural population

Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher-order interactions among large groups of elements have an important role. Here we show, in the vertebrate retina, that weak correlations between pairs of neurons coexist with strongly collective behaviour in the responses of ten or more neurons. We find that this collective behaviour is described quantitatively by models that capture the observed pairwise correlations but assume no higher-order interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or error-correcting properties, and we provide preliminary evidence for such behaviour. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons.     

融合节点影响力与多标签传播的重叠社区发现算法

重叠社区发现是复杂网络分析研究的重要目标之一。针对传统多标签传播算法存在的社区发现结果具有随机性、不稳定性,以及忽视节点影响力对标签传播的影响等问题,提出一种基于节点影响力与多标签传播的能够生成稳定社区的重叠社区发现算法。算法在节点影响力的计算、排序和核心节点识别基础上,通过邻居节点初始标签的再处理和基于平衡系数的节点标签异步更新策略,实现复杂网络重叠社区的有效识别。在真实数据集和人工数据集上的实验综合表明,算法性能优于各对比算法,适用于大规模复杂网络。     

复杂网络研究的经验结果

网络研究已经成为揭示自然界及人类社会各种复杂性系统结构及功能的重要手段.尽管组成真实网络的元素非常不同,网络拓扑也有其自身的复杂性,但大量经验结果显示这些截然不同的网络普遍存在着某些共同性质.因此,要更好地揭示复杂网络的基本性质和功能,我们除了对包含大量元素的复杂系统进行统计外还要对各种不同的网络类型进行分析.这篇论文综述了近年网络研究的成果和进展,归纳复杂网络结构的几个基本性质,包括小世界特征、高聚集性以及确定的连接度分布尤其是无标度度分布行为.     

浅谈动态网页技术

互联网上许多浏览者常对丰富多彩的网页流连忘返 ,赞叹不已 ,但却不知精彩的动态网页为何种技术所制作。本文试图通过各种动态网页技术特点的简单介绍 ,使想要了解这项技术的读者有一个总体的认识。     

支持动态服务组合的Web服务封装

针对如何将包含复杂操作的Web服务封装成Web服务社区和Web服务簇这一问题,提出一种基于Web服务日志,使用序列模式挖掘技术的Web服务封装方法.该方法对Web服务日志进行序列模式挖掘以获得业务功能服务序列,使用获得的序列将Web服务封装成业务功能服务,进而封装成服务社区和服务簇.使用该方法可以有效地将包含复杂操作的Web服务封装成支持动态服务组合的服务社区和服务簇.     

Disentangling nestedness from models of ecological complexity

Complex networks of interactions are ubiquitous and are particularly important in ecological communities, in which large numbers of species exhibit negative (for example, competition or predation) and positive (for example, mutualism) interactions with one another. Nestedness in mutualistic ecological networks is the tendency for ecological specialists to interact with a subset of species that also interact with more generalist species. Recent mathematical and computational analysis has suggested that such nestedness increases species richness. By examining previous results and applying computational approaches to 59 empirical data sets representing mutualistic plant–pollinator networks, we show that this statement is incorrect. A simpler metric—the number of mutualistic partners a species has—is a much better predictor of individual species survival and hence, community persistence. Nestedness is, at best, a secondary covariate rather than a causative factor for biodiversity in mutualistic communities. Analysis of complex networks should be accompanied by analysis of simpler, underpinning mechanisms that drive multiple higher-order network properties.     

信息网络的复杂网络拓扑

综合介绍近几年来在信息网络中所观察到的复杂网络拓扑,包括因特网、WWW网页链和BBS讨论社区的幂律概率分布;对比分析了复杂网络的生长模型及统计模型,并从应用的角度讨论了"小世界"、大群集和容错性等主要的拓扑性质。     

一种基于层次化社团结构的复杂网络可视化平台

基于层次化的网络社团结构,提出了一种可以应用于大型复杂网络的可视化方法,并编程实现了交互平台.该平台采用圆环布局,能提供大量的交互功能,使用户从不同层次上查看网络结构信息.平台还实现了重叠节点的找寻,以及社团动态演化等与网络社团分析有密切关系的功能.     

一种超网络演化模型构建及特性分析

现实世界的很多超网络比如科学家合作超网络,演员合作超网络,WorldWideWeb（WWW）以及引文超网络都具有超边的增长和优先连接机制.基于这个原则,本文构建了一种超网络动态演化模型,并介绍了这个模型的一些基本拓扑性质,如节点度、节点超度、超边的度等.在此演化模型上重点理论分析了超度分布的特性,并进行了仿真实验,发现随着网络规模的增大,这个超网络动态演化模型的超度分布遵循无标度的特性.     

Designing intermediate-range order in amorphous materials

Amorphous materials are commonly understood to consist of random organizations of molecular-type structural units. However, it has long been known that structural organizations intermediate between discrete chemical bonds and periodic crystalline lattices are present even in liquids. Numerous models--including random networks and crystalline-type structures with networks composed of clusters and voids--have been proposed to account for this intermediate-range order. Nevertheless, understanding and controlling structural features that determine intermediate-range order in amorphous materials remain fundamental, yet presently unresolved, issues. The most characteristic signature of such order is the first peak in the total structure factor, referred to as the first sharp diffraction peak or 'low Q' structure. These features correspond to large real-space distances in the materials, and understanding their origin is key to unravelling details of intermediate-range order. Here we employ principles of crystal engineering to design specific patterns of intermediate-range order within amorphous zinc-chloride networks. Using crystalline models, we demonstrate the impact of various structural features on diffraction at low values of Q. Such amorphous network engineering is anticipated to provide the structure/property relationships necessary to tailor specific optical, electronic and mechanical properties.     

旅游目的地虚拟网络结构特征研究——-以黄山市为例

以黄山市为案例, 采用复杂网络理论和方法研究分析目的地虚拟网络的结构特征。结果显示该网络是具有小世界特征的稀疏网络, 其度分布符合幂律分布且幂指数位于1与2之间, 其节点倾向于链接不同类型的节点, 并且节点之间的距离和度值对节点互联的影响较弱。将黄山网络与随机网络、万维网以及其他旅游虚拟网络进行对比分析, 探讨目的地虚拟网络和现实网络之间的关系, 认为虚拟网络不仅只是信息网路, 也是社会网络, 它是现实网络在虚拟空间中的映射。在这个意义下, 目的地虚拟网络的结构特征反映了其现实网络的特征。     

Nonlinear material behaviour of spider silk yields robust webs

Natural materials are renowned for exquisite designs that optimize function, as illustrated by the elasticity of blood vessels, the toughness of bone and the protection offered by nacre. Particularly intriguing are spider silks, with studies having explored properties ranging from their protein sequence to the geometry of a web. This material system, highly adapted to meet a spider's many needs, has superior mechanical properties. In spite of much research into the molecular design underpinning the outstanding performance of silk fibres, and into the mechanical characteristics of web-like structures, it remains unknown how the mechanical characteristics of spider silk contribute to the integrity and performance of a spider web. Here we report web deformation experiments and simulations that identify the nonlinear response of silk threads to stress--involving softening at a yield point and substantial stiffening at large strain until failure--as being crucial to localize load-induced deformation and resulting in mechanically robust spider webs. Control simulations confirmed that a nonlinear stress response results in superior resistance to structural defects in the web compared to linear elastic or elastic-plastic (softening) material behaviour. We also show that under distributed loads, such as those exerted by wind, the stiff behaviour of silk under small deformation, before the yield point, is essential in maintaining the web's structural integrity. The superior performance of silk in webs is therefore not due merely to its exceptional ultimate strength and strain, but arises from the nonlinear response of silk threads to strain and their geometrical arrangement in a web.