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摘要: 复杂系统间的相互作用能够用复杂网络描述. 复杂网络中某些节点遭受攻击或破坏会造成网络故障, 导致整个网络能控性变化. 不同节点失效会对网络能控性有不同的影响. 本文提出一种网络节点的分类方式, 将网络中的节点根据边的方向和匹配关系分成九种类型, 并给出了辨识节点类型的算法. 另外, 本文给出了基于此分类方式下复杂网络中某类节点失效时, 网络中驱动节点数量(用来衡量网络能控性大小的指标)的变化规律. 并通过模型网络进行仿真实验, 验证了当节点失效时本文给出的驱动节点数量变化情况, 同时还分析社交网络中不同类型节点的占比与实际中人际交往的对应关系.Abstract: The interaction between complex systems can be described by complex networks. In complex network, some nodes are attacked or destroyed, which may cause network failure and lead to the change of the whole network controllability. Different node failures have different effects on network controllability. In this paper, a classification method of network nodes is proposed, which divides the nodes into nine types according to the direction of the edge and the matching relationship, and the algorithm for identifying the type of nodes is given. In addition, the change rule of the number of driving nodes is given when a certain type of node fails in the complex network based on this classification method, which is used to measure the controllability of the network. And simulation experiments are carried out through the model network to demonstrate the change of the number of driving nodes given in this paper when the node fails. At the same time, the corresponding relationship between the proportion of different types of nodes in social networks and actual interpersonal communication is also analyzed.
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Key words:
- Complex networks /
- network controllability /
- nodes failure /
- driver node
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图 5 ER网络
$V_{I}$ 和$V_{O}$ 失效可控性变化Fig. 5 Controllability changes of
$V_{I}$ and$V_{O}$ failure in ER networks
图 6 BA网络
$V_{I}$ 和$V_{O}$ 失效可控性变化Fig. 6 Controllability changes of
$V_{I}$ and$V_{O}$ failure in BA networks
图 7 WS网络
$V_{I}$ 和$V_{O}$ 失效可控性变化Fig. 7 Controllability changes of
$V_{I}$ and$V_{O}$ failure in WS networks
图 8 ER网络
$V_{IO}$ 失效可控性变化Fig. 8 Controllability changes of
$V_{IO}$ f ailure in ER networks
图 9 BA网络
$V_{IO}$ 失效可控性变化Fig. 9 Controllability changes of
$V_{IO}$ failure in BA networks
图 10 WS网络
$V_{IO}$ 失效可控性变化Fig. 10 Controllability changes of
$V_{IO}$ failure in WS networks表 1 模型网络不同类型节点占比表
Table 1 Proportion of different types of nodes in the model network
ER网络 BA网络 WS网络 节点数 500 500 500 边数 2485 1968 1000 INM 27 25 0 IM 24 43 0 ONM 24 46 10 OM 31 39 2 INM&ONM 272 266 358 INM&OM 51 48 105 IM&ONM 42 33 20 IM&OM 32 0 5 $ V_{D}$ 0 0 0 
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表 2 实际网络不同类型节点占比表
Table 2 Proportion of different types of nodes in the actual network
经理社交网络 律师社交网络 银行员工社交网络 (1) 银行员工社交网络 (2) 银行员工社交网络 (3) 学生社交网络 (1) 学生社交网络 (2) 节点 21 71 11 11 11 73 73 边 190 892 30 51 27 243 263 $\langle k \rangle$ 9.05 12.56 2.73 4.64 2.54 3.33 3.60 INM 0 1 1 2 1 1 1 IM 3 0 0 0 0 0 0 ONM 0 1 2 0 0 4 4 OM 0 0 1 0 1 2 2 INM&ONM 18 67 3 8 3 44 47 INM&OM 0 2 1 0 3 13 10 IM&ONM 0 0 3 0 2 3 5 IM&OM 0 0 0 0 1 3 0 $V_{D} $ 0 0 0 0 0 3 4
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