Ranking important nodes in complex networks by simulated annealing

In this paper, based on simulated annealing a new method to rank important nodes in complex networks is presented.First, the concept of an importance sequence（IS） to describe the relative importance of nodes in complex networks is defined. Then, a measure used to evaluate the reasonability of an IS is designed. By comparing an IS and the measure of its reasonability to a state of complex networks and the energy of the state, respectively, the method finds the ground state of complex networks by simulated annealing. In other words, the method can construct a most reasonable IS. The results of experiments on real and artificial networks show that this ranking method not only is effective but also can be applied to different kinds of complex networks.

Evolutionary dynamics analysis of complex network with fusion nodes and overlap edges

Multiple complex networks, each with different properties and mutually fused, have the problems that the evolving process is time varying and non-equilibrium, network structures are layered and interlacing, and evolving characteristics are difficult to be measured. On that account, a dynamic evolving model of complex network with fusion nodes and overlap edges（CNFNOEs） is proposed. Firstly, we define some related concepts of CNFNOEs, and analyze the conversion process of fusion relationship and hierarchy relationship. According to the property difference of various nodes and edges, fusion nodes and overlap edges are subsequently split, and then the CNFNOEs is transformed to interlacing layered complex networks（ILCN）. Secondly,the node degree saturation and attraction factors are defined. On that basis, the evolution algorithm and the local world evolution model for ILCN are put forward. Moreover, four typical situations of nodes evolution are discussed, and the degree distribution law during evolution is analyzed by means of the mean field method.Numerical simulation results show that nodes unreached degree saturation follow the exponential distribution with an error of no more than 6%; nodes reached degree saturation follow the distribution of their connection capacities with an error of no more than 3%; network weaving coefficients have a positive correlation with the highest probability of new node and initial number of connected edges. The results have verified the feasibility and effectiveness of the model, which provides a new idea and method for exploring CNFNOE＇s evolving process and law. Also, the model has good application prospects in structure and dynamics research of transportation network, communication network, social contact network,etc.

Evidential method to identify influential nodes in complex networks

Identifying influential nodes in complex networks is still an open issue. In this paper, a new comprehensive centrality mea- sure is proposed based on the Dempster-Shafer evidence theory. The existing measures of degree centrality, betweenness centra- lity and closeness centrality are taken into consideration in the proposed method. Numerical examples are used to illustrate the effectiveness of the proposed method.

Detecting overlapping communities based on vital nodes in complex networks

Detection of community structures in the complex networks is significant to understand the network structures and analyze the network properties. However, it is still a problem on how to select initial seeds as well as to determine the number of communities. In this paper, we proposed the detecting overlapping communities based on vital nodes algorithm（DOCBVA）, an algorithm based on vital nodes and initial seeds to detect overlapping communities. First, through some screening method, we find the vital nodes and then the seed communities through the pretreatment of vital nodes. This process differs from most existing methods, and the speed is faster. Then the seeds will be extended. We also adopt a new parameter of attribution degree to extend the seeds and find the overlapping communities. Finally, the remaining nodes that have not been processed in the first two steps will be reprocessed. The number of communities is likely to change until the end of algorithm. The experimental results using some real-world network data and artificial network data are satisfactory and can prove the superiority of the DOCBVA algorithm.

Rapid identifying high-influence nodes in complex networks

A tiny fraction of influential individuals play a critical role in the dynamics on complex systems. Identifying the influential nodes in complex networks has theoretical and practical significance. Considering the uncertainties of network scale and topology, and the timeliness of dynamic behaviors in real networks, we propose a rapid identifying method（RIM）to find the fraction of high-influential nodes. Instead of ranking all nodes, our method only aims at ranking a small number of nodes in network. We set the high-influential nodes as initial spreaders, and evaluate the performance of RIM by the susceptible-infected-recovered（SIR） model. The simulations show that in different networks, RIM performs well on rapid identifying high-influential nodes, which is verified by typical ranking methods, such as degree, closeness, betweenness,and eigenvector centrality methods.

Identifying influential nodes based on graph signal processing in complex networks

Identifying influential nodes in complex networks is of both theoretical and practical importance. Existing methods identify influential nodes based on their positions in the network and assume that the nodes are homogeneous. However, node heterogeneity （i.e., different attributes such as interest, energy, age, and so on ） ubiquitously exists and needs to be taken into consideration. In this paper, we conduct an investigation into node attributes and propose a graph signal pro- cessing based centrality （GSPC） method to identify influential nodes considering both the node attributes and the network topology. We first evaluate our GSPC method using two real-world datasets. The results show that our GSPC method effectively identifies influential nodes, which correspond well with the underlying ground truth. This is compatible to the previous eigenvector centrality and principal component centrality methods under circumstances where the nodes are homogeneous. In addition, spreading analysis shows that the GSPC method has a positive effect on the spreading dynamics.

Coarse Graining Method Based on Noded Similarity in Complex Network

Coarse graining of complex networks is an important method to study large-scale complex networks, and is also in the focus of network science today. This paper tries to develop a new coarse-graining method for complex networks, which is based on the node similarity index. From the information structure of the network node similarity, the coarse-grained network is extracted by defining the local similarity and the global similarity index of nodes. A large number of simulation experiments show that the proposed method can effectively reduce the size of the network, while maintaining some statistical properties of the original network to some extent. Moreover, the proposed method has low computational complexity and allows people to freely choose the size of the reduced networks.

RESEARCH ON KEY NODES OF WIRELESS SENSOR NETWORK BASED ON COMPLEX NETWORK THEORY

On the basis of complex network theory, the issues of key nodes in Wireless Sensor Networks (WSN) are discussed. A model expression of sub-network fault in WSN is given at first; subsequently, the concepts of average path length and clustering coefficient are introduced. Based on the two concepts, a novel attribute description of key nodes related to sub-networks is proposed. Moreover, in terms of node deployment density and transmission range, the concept of single-point key nodes and generalized key nodes of WSN are defined, and their decision theorems are investigated.

Impulsive synchronization of two coupled complex networks with time-delayed dynamical nodes

In this paper, we investigate the impulsive synchronization between two coupled complex networks with time- delayed dynamical nodes. Based on the Lyapunov stability, the linear feedback control and the impulsive control theories, the linear feedback and the impulsive controllers are designed separately. By using the generalized Barbalat＇s lemma, the global asymptotic impulsive synchronization of the drive-response complex networks is derived and some corresponding sufficient conditions are also obtained. Numerical examples are presented to verify the effectiveness and the correctness of the synchronization criteria.

基于PSNodeRank算法的电力系统关键节点辨识方法

电力系统中的某些关键节点在系统发生大规模连锁故障的时候可能会对故障的扩大起着推动的作用。为了提高关键节点辨识的速度和准确性,该文通过对Google公司提出的PageRank算法进行改进,提出基于PSNodeRank算法的电网关键节点辨识方法。该方法选取电网关键节点的重要评价指标,建立电力系统有向加权网络模型。考虑电力系统网络的网络链接方向和权值的特性,该文提出PSNodeRank值对节点进行评估,并具体描述每个节点的重要性,再利用电力系统分区特点,对大电网节点重要性的复杂计算过程进行改进,大大提高了运算速度,减少了运算所需存储容量。最后,通过对IEEE 39节点系统进行仿真,所得结果表明:该文所提方法计算的指标可以有效、准确地辨识出电网中的关键节点,判断它们在交直流电网自组织临界演化过程中的作用。对预防系统向连锁故障临界状态演化有着重要的意义。

Circulation system complex networks and teleconnections

In terms of the characteristic topology parameters of climate complex networks, the spatial connection structural complexity of the circulation system and the influence of four teleconnection patterns are quantitatively described. Results of node degrees for the Northern Hemisphere （NH） mid-high latitude （30° N-90°N） circulation system （NHS） networks with and without the Arctic Oscillations （AO）, the North Atlantic Oscillations （NAO） and the Pacific-North American pattern （PNA） demonstrate that the teleconnections greatly shorten the mean shortest path length of the networks, thus being advantageous to the rapid transfer of local fluctuation information over the network and to the stability of the NHS. The impact of the AO on the NHS connection structure is most important and the impact of the NAO is the next important. The PNA is a relatively independent teleconnection, and its role in the NHS is mainly manifested in the connection between the NHS and the tropical circulation system （TRS）. As to the Southern Hemisphere mid-high latitude （30°S-90°S） circulation system （SHS）, the impact of the Antarctic Arctic Oscillations （AAO） on the structural stability of the system is most important. In addition, there might be a stable correlation dipole （AACD） in the SHS, which also has important influence on the structure of the SHS networks.

Vital Nodes Evolution Study on Railway Network of Silk Road Economic Belt

In order to study the nodes importance and its evolution process of the railway network of SREB (Silk Road Economic Belt), we construct the network (RNSREB) based on Graph Theory, which focuses on the time intervals according to actually railway network, railway project under construction and the national railway network of medium-and long-term plan. The algorithms for vital nodes evaluation are analyzed, the evaluation method on nodes importance of RNSREB is proposed, the quantized values of each node are calculated with Pajek, and TOP20 core nodes of the network with different coefficients and time intervals are determined respectively. Then the evolution process of TOP20 critical nodes with 4 periods is contrasted and analyzed. It is indicated that some vital nodes newly discovered (Geermu, Maduo, Ruoqiang) should be concerned.

基于邻域K-shell分布的关键节点识别方法

复杂网络中关键节点的精准识别对于网络结构稳定和信息传播起着至关重要的作用。传统K-shell方法仅通过节点在网络中所处位置对节点的重要性进行评估,导致区分度不高。基于此,综合考虑了节点的全局信息和局部信息对节点重要性的影响,提出一种基于邻域K-shell分布的关键节点识别方法。该方法通过节点邻域Ks值定义节点的熵,从而反映邻居节点的K-shell分布特征。通过11个网络数据集上的仿真实验,验证了所提方法能够更准确地识别并区分复杂网络中的关键节点。

航空器场面滑行关键路径识别与抗毁性研究

为准确辨识机场地面滑行系统重要路段,提升拥塞风险控制能力,通过构建机场活动区交通网络模型,从节点近邻、全局路径、特征向量和网络位置4个角度挖掘关键节点,提出改进介数中心性算法,得到节点重要度排序样例集。综合鲁棒性、性能下降速率以及单位时间性能损失等网络性能指标,通过抗毁性实验分析性能变化曲线,确定综合抗毁性衡量指标ki测度下复杂网络节点重要度排序结果,实现关键路径识别。以华北某机场为例开展实证研究,结果表明:机场活动区交通网络具有较小的聚类系数,在随机攻击下抗毁性较强,基于度中心性的节点序列为所有样例中最满足实际运行中的关键路段,管制员可实施重点路段流量调配,抑制冲突。

西安城市展示中心长悬挑、大跨度钢结构设计

西安城市展示中心由南馆、北馆和连桥组成,其中南馆悬挑长度62m,连桥跨度150m。结合建筑方案特点,南馆与连桥采用整层钢桁架结构体系,结构布置与建筑形态高度契合。介绍了南馆、连桥、穹顶、屋面等位置的结构布置情况,明确了超限项和抗震性能目标,对于多杆件复杂交汇钢节点进行有限元分析。针对南馆、连桥屋楼盖振动舒适度不足,设计布置了调谐质量阻尼器(TMD),实测减振效果显著。对连桥提升过程进行施工模拟,结果表明该过程增加了连桥挠度,需要考虑提前起拱。对超长连体结构温度和地震行波效应进行分析,根据结果对连桥楼板配筋和局部框架柱进行了加强。大震弹塑性分析与防连续倒塌分析结果表明,结构满足“大震不倒”的性能目标,结构冗余度较高,具有良好的防连续倒塌能力。

水网结构对多灾害情景的韧性响应研究

通过识别基础设施系统内部重要节点以提高基础设施韧性,对增强城市韧性具有重要意义。水网作为基础设施的重要组成部分,对水资源统筹调配与水旱灾害防控等发挥着重要作用。基于复杂网络理论,构建水网网络拓扑结构,计算水网各节点参数与灾害风险度,采用不同节点攻击策略,使用随机攻击、蓄意攻击和自然灾害3种攻击方式,得到整体网络效率与最大连通子图大小,对水网韧性进行分析。研究结果表明:水网结构遭到随机攻击或自然灾害时,破坏节点达80%左右,水网韧性趋近于0;水网结构遭到蓄意攻击时,破坏节点达50%左右,水网结构系统崩溃;在蓄意攻击中,PageRank攻击对水网韧性影响较大;在自然灾害攻击中,水网结构在面对暴雨洪涝时表现出较强的韧性。在网络拓扑结构研究水平的基础上,在工程真实物理状态下对水网结构遭到随机攻击、蓄意攻击与自然灾害后的水网韧性进行了更全面的分析与评价,为水网工程建设与管理研究提供参考。

基于深度强化学习的复杂网络节点影响力排序算法

针对当前节点影响力评估算法准确度较低的情况,提出了一种基于深度强化学习的节点影响力排序算法。该算法从网络拆解的视角看待节点影响力,将节点影响力的排序问题转换为网络拆除策略的优化问题。算法首先利用排序学习训练图神经网络模型的节点特征提取能力,然后使用强化学习对依赖于网络状态的节点断连行为做价值学习,最后使用训练完成的模型预测网络拆除的最佳策略,即节点影响力的最准确排序。仿真实验证明,所提算法在典型真实数据集的CN(Crtical Node)与ND(Network Dismantling)问题上,相较于PageRank算法,准确度分别提升了31.1%与29.0%。同时,该算法具有较低的复杂度,可为网络稳定性分析和网络性能优化提供技术支撑。

基于光学定位的三维超声引导肌肉注射仪设计研究

目的解决光学定位技术在引入肌肉痉挛治疗的注射手术应用中,光学定位设备与现有医用超声仪器之间的不适配问题,旨在进一步提升理论定位精度稳定性,简化必需操作并降低实际应用难度。方法在现有超声仪及相关设备功能基础上,结合光学定位设备工作条件需求进行需求分析,重新构建产品元件功能流模型并映射为网络节点,并基于复杂网络节点重要度评价方法,确定目标产品设计重心点并分层设计,最后采用仿真验证测试设计合理性。结果实验结果符合预期假设,目标节点所对应功能元件与其它节点的相关性程度与目标元件所需兼容连接的复杂度呈正相关。基于实验得出能够适配光学定位仪与超声设备的设计方案,有效解决二维超声导航引导肌肉注射所面临的不直观、不可视等问题。结论基于复杂网络节点的重要度评价方法更适用于复杂功能产品的设计研究,评价结果重要度差异更为显著。

基于关键节点积极效应模型的快递物流网络点集挖掘

针对快递物流网络中点集挖掘问题,基于关键节点积极效应模型构建DW-KPP-Pos模型,并设计一种启发式算法提升模型运算效率。对中国快递物流网络的实证分析表明:融合启发式算法的DW-KPP-Pos模型可高效挖掘快递物流网络中的“最大传播点集”,该集合成员包括上海市、重庆市、广州市、北京市、金华市和香港特别行政区;计量结果对比显示,DW-KPP-Pos模型所挖掘的点集K,相对点度数点集K deg、PageRank点集K pag和中介中心性点集K bet,传播效率分别高出0.59%、0.88%和6.19%。

基于层级划分和节点特征的关键节点识别方法

关键节点识别已经成为复杂网络领域的一个重要研究范畴,但目前关键节点识别方法存在时间复杂度较高、得到的关键节点集不够准确以及节点中心性指标考虑不够充分等问题。基于此,提出一种基于层级划分和节点特征的关键节点识别框架,在该框架内,为避免选取节点初始覆盖集时效率低下的问题,提出一种基于层级划分的关键节点初始覆盖集选取方法,该方法可在线性时间内计算出初始节点覆盖集,随后通过节点中心性指标向原网络中回添节点,直到解集中的节点数满足预定义阈值数。为解决回添节点过程中易陷于局部最优解的问题,综合考虑网络拓扑结构和节点的多种属性,提出一种节点综合特征的中心性指标。对比5种初始覆盖集选取算法以及5个中心性指标,在真实网络上进行方法的应用和分析,结果表明,所提基于层级划分和节点特征的方法能够在不同类型的网络中更准确有效地识别关键节点,且该方法的鲁棒性更好,性能也优于其他方法。