Hierarchical Characterization of Complex Networks

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work considers the concept of virtual hierarchies established around each node and the respectively defined hierarchical node degree and clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.     

利用节点效率评估复杂网络功能鲁棒性

为了克服现有复杂网络鲁棒性研究模型只考虑节点失效的局部影响性和网络拓扑鲁棒性的缺陷, 提出了一种利用节点效率来评估复杂网络功能鲁棒性的方法. 该方法综合考虑节点失效的全局影响性, 利用网络中节点的效率来定义各节点的负载、极限负载和失效模型, 通过打击后网络中最终失效节点的比例来衡量网络的功能鲁棒性, 并给出了其评估优化算法. 实验分析表明该方法对考虑节点负载的复杂网络功能鲁棒性的评定可行有效, 对于大型复杂网络可以获得理想的计算能力.     

The emergence of scale-free networks with a seceding mechanism

In order to explore further the underlying mechanism of scale-free networks, we study stochastic secession as a mechanism for the creation of complex networks. In this evolution the network growth incorporates the addition of new nodes, the addition of new links between existing nodes, the deleting and rewiring of some existing links, and the stochastic secession of nodes. To random growing networks with preferential attachment, the model yields scale-free behavior for the degree distribution. Furthermore, we obtain an analytical expression of the power-law degree distribution with scaling exponent γ ranging from 1.1 to 9. The analytical expressions are in good agreement with the numerical simulation results.     

基于区域密度曲线识别网络上的多影响力节点

复杂网络多影响力节点的识别可以帮助理解网络的结构和功能,具有重要的理论意义和应用价值.本文提出一种基于网络区域密度曲线的多影响力节点的识别方法.应用两种不同的传播模型,在不同网络上与其他中心性指标进行了比较.结果表明,基于区域密度曲线的识别方法能够更好地识别网络中的多影响力节点,选中的影响力节点之间的分布较为分散,自身也比较重要.本文所提方法是基于网络的局部信息,计算的时间复杂度较低.     

Concentric characterization and classification of complex network nodes: Application to an institutional collaboration network

Differently from theoretical scale-free networks, most real networks present multi-scale behavior, with nodes structured in different types of functional groups and communities. While the majority of approaches for classification of nodes in a complex network has relied on local measurements of the topology/connectivity around each node, valuable information about node functionality can be obtained by concentric (or hierarchical) measurements. This paper extends previous methodologies based on concentric measurements, by studying the possibility of using agglomerative clustering methods, in order to obtain a set of functional groups of nodes, considering particular institutional collaboration network nodes, including various known communities (departments of the University of São Paulo). Among the interesting obtained findings, we emphasize the scale-free nature of the network obtained, as well as identification of different patterns of authorship emerging from different areas (e.g. human and exact sciences). Another interesting result concerns the relatively uniform distribution of hubs along concentric levels, contrariwise to the non-uniform pattern found in theoretical scale-free networks such as the BA model.     

Jamming transition in air transportation networks

In this work we present a model of an air transportation traffic system from the complex network modelling viewpoint. In the network, every node corresponds to a given airport, and two nodes are connected by means of flight routes. Each node is weighted according to its load capacity, and links are weighted according to the Euclidean distance that separates each pair of nodes. Local rules describing the behaviour of individual nodes in terms of the surrounding flow have been also modelled, and a random network topology has been chosen in a baseline approach. Numerical simulations describing the diffusion of a given number of agents (aircraft) in this network show the onset of a jamming transition that distinguishes an efficient regime with null amount of airport queues and high diffusivity (free phase) and a regime where bottlenecks suddenly take place, leading to a poor aircraft diffusion (congested phase). Fluctuations are maximal around the congestion threshold, suggesting that the transition is critical. We then proceed by exploring the robustness of our results in neutral random topologies by embedding the model in heterogeneous networks. Specifically, we make use of the European air transportation network formed by 858 airports and 11 170 flight routes connecting them, which we show to be scale-free. The jamming transition is also observed in this case. These results and methodologies may introduce relevant decision-making procedures in order to optimize the air transportation traffic.     

基于复杂网络理论的北京公交网络拓扑性质分析

为分析公交复杂网络的拓扑性质, 本文以北京市为例, 选取截止到2010年7月的北京全市(14区、2县)的1165条公交线路和9618个公交站点为样本数据, 运用复杂网络理论构建起基于邻接站点的有向加权复杂网络模型. 该方法以公交站点作为节点, 相邻站点之间的公交线路作为边, 使得网络既具有复杂网络的拓扑性质同时节点(站点)又具有明确的地理坐标. 对网络中节点度、点强度、强度分布、平均最短路径、聚类系数等性质的分析显示, 公交复杂网络的度和点强度分布极为不均, 网络中前5%和前10%节点的累计强度分布分别达到22.43%和43.02%; 点强度与排列序数、累积强度分布都服从幂律分布, 具有无标度和小世界的网络特点, 少数关键节点在网络中发挥着重要的连接作用. 为分析复杂网络中的关键节点, 本文通过承载压力分析和基于"掠夺" 的区域中心节点提取两种方法, 得到了公交复杂网络中两类不同表现的关键节点. 这些规律也为优化城市公交网络及交通规划发展提供了新的参考建议.     

The signal synchronization transmission of a spatiotemporal chaos network constituted by a laser phase-conjugate wave

The signal synchronization transmission of a spatiotemporal chaos network is investigated.The structure of the coupling function between connected nodes of the complex network and the value range of the linear term coefficient of the separated configuration in state equation of the node are obtained through constructing an appropriate Lyapunov function.Each node of the complex network is a laser spatiotemporal chaos model in which the phase-conjugate wave and the unilateral coupled map lattice are taken as a local function and a spatially extended system,respectively.The simulation results show the effectiveness of the signal synchronization transmission principle of the network.     

Communicability betweenness in complex networks

Betweenness measures provide quantitative tools to pick out fine details from the massive amount of interaction data that is available from large complex networks. They allow us to study the extent to which a node takes part when information is passed around the network. Nodes with high betweenness may be regarded as key players that have a highly active role. At one extreme, betweenness has been defined by considering information passing only through the shortest paths between pairs of nodes. At the other extreme, an alternative type of betweenness has been defined by considering all possible walks of any length. In this work, we propose a betweenness measure that lies between these two opposing viewpoints. We allow information to pass through all possible routes, but introduce a scaling so that longer walks carry less importance. This new definition shares a similar philosophy to that of communicability for pairs of nodes in a network, which was introduced by Estrada and Hatano [E. Estrada, N. Hatano, Phys. Rev. E 77 (2008) 036111]. Having defined this new communicability betweenness measure, we show that it can be characterized neatly in terms of the exponential of the adjacency matrix. We also show that this measure is closely related to a Fréchet derivative of the matrix exponential. This allows us to conclude that it also describes network sensitivity when the edges of a given node are subject to infinitesimally small perturbations. Using illustrative synthetic and real life networks, we show that the new betweenness measure behaves differently to existing versions, and in particular we show that it recovers meaningful biological information from a protein-protein interaction network.     

Vibro-acoustic control with a distributed sensor network

The purpose of this work is to demonstrate the ability of a distributed control system, based on a smart sensor network, to reduce acoustic radiation from a vibrating structure. The platform from which control is effected consists of a network of smart sensors, each referred to as a node. Each node possesses its own computational capability, sensor, actuator and the ability to communicate with other nodes via a wired or wireless network. The primary focus of this work is to employ existing group management middleware concepts to enable vibro-acoustic control with such a distributed network. Group management middleware is distributed software that provides for the establishment and maintenance of groups of distributed nodes and that provides for the network communication among such groups. The control objective is met by designing distributed feedback compensators that take advantage of node groups in order to effect their control. The node groups are formed based on physical proximity. The global control objective is to minimize the radiated sound power from a rectangular plate. Results of this investigation demonstrate that such a distributed control system can achieve attenuations comparable to those achieved by a centralized controller.     

基于节点间依赖度的社团结构划分方法

本文提出了一种基于节点间依赖度的在复杂网络中划分社团结构的算法,定义了节点对其邻居的依赖度以及节点对社团的依赖度和条件依赖度.算法的基本要点是优先将最大依赖度不小于其他节点且有惟一依赖节点的节点划分到社团,并将对社团的依赖度或条件依赖度达到一定值的节点吸收进社团,直到所有节点都得到准确的社团划分.本算法在几个实际网络的测试上,都成功地划分出了满足条件的社团,并且对社团结构已知的网络的划分结果符合实际情况.     

Scalably Using Node Attributes and Graph Structure for Node Classification

The task of node classification concerns a network where nodes are associated with labels, but labels are known only for some of the nodes. The task consists of inferring the unknown labels given the known node labels, the structure of the network, and other known node attributes. Common node classification approaches are based on the assumption that adjacent nodes have similar attributes and, therefore, that a node’s label can be predicted from the labels of its neighbors. While such an assumption is often valid (e.g., for political affiliation in social networks), it may not hold in some cases. In fact, nodes that share the same label may be adjacent but differ in their attributes, or may not be adjacent but have similar attributes. In this work, we present JANE (Jointly using Attributes and Node Embeddings), a novel and principled approach to node classification that flexibly adapts to a range of settings wherein unknown labels may be predicted from known labels of adjacent nodes in the network, other node attributes, or both. Our experiments on synthetic data highlight the limitations of benchmark algorithms and the versatility of JANE. Further, our experiments on seven real datasets of sizes ranging from 2.5K to 1.5M nodes and edge homophily ranging from 0.86 to 0.29 show that JANE scales well to large networks while also demonstrating an up to 20% improvement in accuracy compared to strong baseline algorithms.     

Improvement of Delegated Proof of Stake Consensus Mechanism Based on Vague Set and Node Impact Factor

The Delegated Proof of Stake (DPoS) consensus mechanism uses the power of stakeholders to not only vote in a fair and democratic way to solve a consensus problem, but also reduce resource waste to a certain extent. However, the fixed number of member nodes and single voting type will affect the security of the whole system. In order to reduce the negative impact of the above problems, a new consensus algorithm based on vague set and node impact factors is proposed. We first use fuzzy values to calculate the ratings of all nodes and initially determine the number of agent nodes according to the preset threshold value. Then, we judge whether a secondary screening is needed. If needed, calculating the nodes’ impact factor based on their neighboring nodes, and combining their impact factors with adjacency votes to further distinguish the nodes with the same fuzzy value. In addition, we analyze the dynamic changes in the composition and scale of the agent node set and give its ideal size through testing. Finally, we compare the proposed algorithm with DPoS algorithm and existing fuzzy set-based algorithms in different scales and network structures. Results show that no matter in what kind of network structures, the effectiveness of the proposed algorithm is improved. Among which, the most noticeable improvement is seen in complex network structures.     

Cascading Failures of Complex Networks Based on Two-Step Degree

We propose a new concept, two-step degree. Defining it as the capacity of a node of complex networks, we establish a novel capacity-load model of cascading failures of complex networks where the capacity of nodes decreases during the process of cascading failures. For scale-free networks, we find that the average two-step degree increases with the increase of the heterogeneity of the degree distribution, showing that the average two- step degree can be used for measuring the heterogeneity of the degree distribution of complex networks. In addition, under the condition that the average degree of a node is given, we can design a scale-free network with the optimal robustness to random failures by maximizing the average two-step degree.     

基于节点相关性的网络不动点理论研究

现代复杂的通信网络内部存在着广泛的幂律现象，网络节点之间存在相关特性. 根据这种相关特性，提出了网络不动点理论. 将Banach不动点理论引入网络模型，证明了网络不动点理论的正确有效性. 证明过程是把通信网络看作由路径预测算法产生的似马尔可夫链的路由节点迭代序列形成的网络空间. 由节点相关性可知，此空间中的节点序列相对越长就越能折射出搜索的目标所在，预测准确率也会逐步增加，可以更好地进行目标定位、数据挖掘等. 通过某种路由准则的算子从源节点最终映射到的目的节点与Banach空间的不动点相对应，即为网络空间的不动点. 当网络发展到能为用户提供真正的无处不在的连接时，网络不动点理论的物理特性将非常明显. 因为网络规模越大，节点间的群体作用越显著，就越能显现网络不动点理论的物理特性. 关键词： 计算机网络 长程相关 不动点 幂律     

基于局部路由策略的复杂网络拥塞控制

提出一种复杂网络上的局部路由策略,算法采用节点收缩法评估节点的重要度,发送节点根据邻居节点的重要度及网络的状态自适应地调整向邻居节点转发数据包的概率.在网络处于自由流通状态时充分发挥关键节点的优势,保证数据包快速到达目的地;在网络处于即将拥塞时分散业务,根据节点重要度准确识别网络中的关键节点,通过有效分流予以保护.仿真结果表明:在网络处于自由流通状态时,该局部路由策略能充分发挥网络中关键节点的枢纽作用,保持较低的传输时延;在网络部分关键节点出现拥塞时,该局部路由策略能有效避开拥挤严重的节点,将数据包均匀地分布在各个节点上,有效抑制网络拥塞,提高网络的容量.     

Network robustness to targeted attacks. The interplay of expansibility and degree distribution

We study the property of certain complex networks of being both sparse and highly connected, which is known as “good expansion” (GE). A network has GE properties if every subset S of nodes (up to 50% of the nodes) has a neighborhood that is larger than some “expansion factor” φ multiplied by the number of nodes in S. Using a graph spectral method we introduce here a new parameter measuring the good expansion character of a network. By means of this parameter we are able to classify 51 real-world complex networks — technological, biological, informational, biological and social — as GENs or non-GENs. Combining GE properties and node degree distribution (DD) we classify these complex networks in four different groups, which have different resilience to intentional attacks against their nodes. The simultaneous existence of GE properties and uniform degree distribution contribute significantly to the robustness in complex networks. These features appear solely in 14% of the 51 real-world networks studied here. At the other extreme we find that ∼40% of all networks are very vulnerable to targeted attacks. They lack GE properties, display skewed DD — exponential or power-law — and their topologies are changed more dramatically by targeted attacks directed at bottlenecks than by the removal of network hubs.     

基于自规避随机游走的节点排序算法

评估复杂网络系统的节点重要性有助于提升其系统抗毁性和结构稳定性. 目前, 定量节点重要性的排序算法通常基于网络结构的中心性指标如度数、介数、紧密度、特征向量等. 然而, 这些算法需要以知晓网络结构的全局信息为前提, 很难在大规模网络中实际应用. 基于自规避随机游走的思想, 提出一种结合网络结构局域信息和标签扩散的节点排序算法. 该算法综合考虑了节点的直接邻居数量及与其他节点之间的拓扑关系, 能够表征其在复杂网络系统中的结构影响力和重要性. 基于三个典型的实际网络, 通过对极大连通系数、网络谱距离数、节点连边数和脆弱系数等评估指标的实验对比, 结果表明提出的算法显著优于现有的依据局域信息的节点排序算法.     

一种基于效率矩阵的网络节点重要度评价算法

为了实现对网络节点重要性的有效评价,提出一种基于网络效率矩阵的节点重要度评价算法.该方法综合考虑节点的度值(局部重要度)和网络节点之间的重要性贡献(全局重要度),利用节点的度和效率矩阵表征网络节点的重要度贡献,克服重要性贡献矩阵法中节点只依赖于邻接节点的不足.考虑实际网络的稀疏性,该算法的时间复杂度为O(n²).通过算例分析验证了该算法的可行性和有效性,结果表明:该算法能够更加直观、简单有效地区分节点的重要度差异,并且对于大型复杂网络具有较理想的计算能力.     

Geographical Effects on Complex Networks

We investigate how the geographical structure of a complex network affects its network topology, synchronization and the average spatial length of edges. The geographical structure means that the connecting probability of two nodes is related to the spatial distance of the two nodes. Our simulation results show that the geographical structure changes the network topology. The synchronization tendency is enhanced and the average spatial length of edges is enlarged when the node can randomly connect to the further one. Analytic results support our understanding of the phenomena.