异质依存网络衰退特征与关键节点辨识
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摘要
针对传统复杂网络理论通常以同质单层网络作为研究对象,忽视现有工业复杂网络具有多异质节点与多层网络互耦合性的问题,提出异质依存网络(Heterogeneous-interdependent network,HI net)理论及其关键节点辨识方法.以含多类型节点的异质依存网络作为研究对象,分析异质节点依存关系以及网络衰退机理.构建分块结构下异质节点依存矩阵,将多层异质依存网络归并于单层网络.提出节点效用耦合系数,描述不同故障类型下邻居节点效用耦合性.建立节点邻域效用耦合系数计算方法及其影响力传播方法,识别节点对网络状态的影响,实现关键节点识别.通过对典型的含多电源电网系统与电力信息物理异质依存网络进行仿真实验,分别验证了所提方法对不同故障类型下关键节点识别的有效性.
In order to solve the problem that traditional complex network theory usually takes homogeneous single-layer network as research object, and neglects mutual coupling relations among heterogeneous nodes or multi-layer networks in industrial complex networks, the heterogeneous-interdependent network(HI net) theory with key node identification method is proposed. Taking the HI net with multi types of nodes as the object,we study the dependency relations of nodes and the mechanism of network degeneration. Then, the dependency matrix of heterogeneous nodes is established to combine the multi-layer HI networks into one layer. To describe the effectiveness coupling for neighboring node under different fault mode, the effectiveness coupling coefficient is designed. Finally, the effectiveness coupling coefficient of neighborhood nodes and its propagation method are given to calculate the influence from node to networks to identify the key nodes in HI net. The effectiveness of the key nodes identification method is verified by the simulations of two typical HI nets, including the power system with multi generations and power-information HI net.
In order to solve the problem that traditional complex network theory usually takes homogeneous single-layer network as research object, and neglects mutual coupling relations among heterogeneous nodes or multi-layer networks in industrial complex networks, the heterogeneous-interdependent network(HI net) theory with key node identification method is proposed. Taking the HI net with multi types of nodes as the object,we study the dependency relations of nodes and the mechanism of network degeneration. Then, the dependency matrix of heterogeneous nodes is established to combine the multi-layer HI networks into one layer. To describe the effectiveness coupling for neighboring node under different fault mode, the effectiveness coupling coefficient is designed. Finally, the effectiveness coupling coefficient of neighborhood nodes and its propagation method are given to calculate the influence from node to networks to identify the key nodes in HI net. The effectiveness of the key nodes identification method is verified by the simulations of two typical HI nets, including the power system with multi generations and power-information HI net.
引文
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7 Zhao L,Park K,Lai Y C.Attack vulnerability of scale-free networks due to cascading breakdown.Physical Review E,2004,70(2):Article No.035101
8 Tang L,Jing K,He J,Stanley H E.Complex interdependent supply chain networks:cascading failure and robustness.Physica A:Statistical Mechanics and Its Applications,2016,443:58-69
9 Xie Feng,Cheng Su-Qi,Chen Dong-Qing,Zhang GuoQiang.Cascade-based attack vulnerability in complex networks.Journal of Tsinghua University(Science&Technology),2011,51(10):1252-1257(谢丰,程苏琦,陈冬青,张国强.基于级联失效的复杂网络抗毁性.清华大学学报(自然科学版),2011,51(10):1252-1257)
10 Buldyrev S V,Parshani R,Paul G,Stanley H E,Havlin S.Catastrophic cascade of failures in interdependent networks.Nature,2010,464(7291):1025-1028
11 Gao J X,Buldyrev S V,Stanley H E,Havlin S.Networks formed from interdependent networks.Nature Physics,2012,8(1):40-48
12 Sun Y Z,Han J W,Yan X F,Yu P S,Wu T Y.Path Sim:meta path-based top-k similarity search in heterogeneous information networks.Proceedings of the VLDB Endowment,2011,4(11):992-1003
13 Boldi P,Santini M,Vigna S.Page Rank:functional dependencies.ACM Transactions on Information Systems,2009,27(4):Article No.19
14 Eom Y H,Shepelyansky D L.Opinion formation driven by Page Rank node influence on directed networks.Physica A:Statistical Mechanics and Its Applications,2015,436:707-715
15 Wu X D,Kumar V,Quinlan J R,Ghosh J,Yang Q,et al.Top 10 algorithms in data mining.Knowledge and Information Systems,2008,14(1):1-37
16 Pai M A.Energy Function Analysis for Power System Stability.London:Kluwer Academic Publishers,1989.
17 Wang K,Zhang B H,Zhang Z,Yin X G,Wang B.An electrical betweenness approach for vulnerability assessment of power grids considering the capacity of generators and load.Physica A:Statistical Mechanics and Its Applications,2011,390(23-24):4692-4701
18 Arianos S,Bompard E,Carbone A,Xue F.Power grid vulnerability:a complex network approach.Chaos,2009,19(1):Article No.013119
2 Wei Xiang,Zhao Jun-Chan,Hu Chun-Hua.Generalized synchronization and system parameters identification between two different complex networks.Acta Automatica Sinica,2017,43(4):595-603(韦相,赵军产,胡春华.两个异构复杂网络的广义同步与参数识别.自动化学报,2017,43(4):595-603)
3 Xie Qiong-Yao,Deng Chang-Hong,Zhao Hong-Sheng,Weng Yi-Xuan.Evaluation method for node importance of power grid based on the weighted network model.Automation of Electric Power Systems,2009,33(4):21-24(谢琼瑶,邓长虹,赵红生,翁毅选.基于有权网络模型的电力网节点重要度评估.电力系统自动化,2009,33(4):21-24)
4 Yu Xin,Li Yan-He,Zheng Xiao-Ping,Zhang Han-Yi,Guo Yi-Li.Node importance evaluation based on communication network performance grads.Journal of Tsinghua University(Science&Technology),2008,48(4):541-544(余新,李艳和,郑小平,张汉一,郭奕理.基于网络性能变化梯度的通信网络节点重要程度评价方法.清华大学学报(自然科学版),2008,48(4):541-544)
5 Fu Xiu-Wen,Li Wen-Feng,Duan Ying.Invulnerability of clustering wireless sensor network towards cascading failures.Journal of Computer Research and Development,2016,53(12):2882-2892(符修文,李文锋,段莹.分簇无线传感器网络级联失效抗毁性研究.计算机研究与发展,2016,53(12):2882-2892)
6 Wu Run-Ze,Zhang Bao-Jian,Tang Liang-Rui.A cascading failure based nodal importance evaluation method applied in dual network coupling model.Power System Technology,2015,39(4):1053-1058(吴润泽,张保健,唐良瑞.双网耦合模型中基于级联失效的节点重要度评估.电网技术,2015,39(4):1053-1058)
7 Zhao L,Park K,Lai Y C.Attack vulnerability of scale-free networks due to cascading breakdown.Physical Review E,2004,70(2):Article No.035101
8 Tang L,Jing K,He J,Stanley H E.Complex interdependent supply chain networks:cascading failure and robustness.Physica A:Statistical Mechanics and Its Applications,2016,443:58-69
9 Xie Feng,Cheng Su-Qi,Chen Dong-Qing,Zhang GuoQiang.Cascade-based attack vulnerability in complex networks.Journal of Tsinghua University(Science&Technology),2011,51(10):1252-1257(谢丰,程苏琦,陈冬青,张国强.基于级联失效的复杂网络抗毁性.清华大学学报(自然科学版),2011,51(10):1252-1257)
10 Buldyrev S V,Parshani R,Paul G,Stanley H E,Havlin S.Catastrophic cascade of failures in interdependent networks.Nature,2010,464(7291):1025-1028
11 Gao J X,Buldyrev S V,Stanley H E,Havlin S.Networks formed from interdependent networks.Nature Physics,2012,8(1):40-48
12 Sun Y Z,Han J W,Yan X F,Yu P S,Wu T Y.Path Sim:meta path-based top-k similarity search in heterogeneous information networks.Proceedings of the VLDB Endowment,2011,4(11):992-1003
13 Boldi P,Santini M,Vigna S.Page Rank:functional dependencies.ACM Transactions on Information Systems,2009,27(4):Article No.19
14 Eom Y H,Shepelyansky D L.Opinion formation driven by Page Rank node influence on directed networks.Physica A:Statistical Mechanics and Its Applications,2015,436:707-715
15 Wu X D,Kumar V,Quinlan J R,Ghosh J,Yang Q,et al.Top 10 algorithms in data mining.Knowledge and Information Systems,2008,14(1):1-37
16 Pai M A.Energy Function Analysis for Power System Stability.London:Kluwer Academic Publishers,1989.
17 Wang K,Zhang B H,Zhang Z,Yin X G,Wang B.An electrical betweenness approach for vulnerability assessment of power grids considering the capacity of generators and load.Physica A:Statistical Mechanics and Its Applications,2011,390(23-24):4692-4701
18 Arianos S,Bompard E,Carbone A,Xue F.Power grid vulnerability:a complex network approach.Chaos,2009,19(1):Article No.013119