首页 > 科学研究 > 学术动态
[成果] 复杂网络中的靶向修复

研究成果:Sun, W., Zeng, A. European Physical Journal B (2017). doi: 10.1140/epjb/e2016-70618-0







The invulnerability of complex networks is an important issue which has been widely analyzed in different fields. A lot of works have been done to measure and improve the stability of complex networks when being attacked. Recently, how to recover networks after attack was intensively studied. The existing methods are mainly designed to recover the overall functionality of networks, yet in many real cases the recovery of important nodes should be given priority, to which we refer target recovery. For example, when the cold wave paralyses the railway networks, target recovery means to repair those stations or railways such that the transport capacity of densely-populated cities can be recovered as fast as possible. In this paper, we first compare the impact of attacks on the whole network and target nodes respectively, and then study the efficiency of traditional recovery methods that are proposed based on global centrality metrics. Furthermore, based on target centrality metrics, we introduce a local betweenness recovery method and we find it has better performance than the traditional methods. We finally propose a hybrid recovery method which includes local betweenness metric and local closeness metric. The performance of the hybrid method is shown to be similar to that of the greedy algorithm.






Fig. 1. Illustration of target recovery in complex networks. The network above is world airlines network and the green lines represent the airlines. Red circles, green circles and blue circles correspond to failure nodes, healthy nodes and target nodes respectively.

Fig. 2. The dependence of transportation efficiency of four kinds of targets (i.e., globalized targets, localized targets, small degree targets and large degree targets) on the number of failure nodes (random attacks) in different networks (logarithmic coordinate in Y axis).

Fig. 3. (a, b) The transportation efficiency with different ratios of target nodes and different random recovery ratios in BA and lattice network respectively; (c, d) the transportation efficiency of target nodes when the network is 20% repaired by different recovery methods in BA and lattice network respectively.

Fig. 4. (a, b) The local betweenness and local closeness of every failure nodes. The yellow circles represent first few repaired nodes in greedy recovery. The black dots stand for the rest of failure nodes (logarithmic coordinate in X axis). (c, d) The dependence of transportation efficiency on hybrid index λ when the network is 20% repaired.

Fig. 5. The recovery effect of local betweenness recovery (LBR), greedy recovery (GR), and hybrid recovery (HR) in BA, lattice, power grid and world air network respectively.

Table 1. The basic structural properties of real networks, and their transportation efficiency η when 20% repaired by different recovery methods. Structural propertes include network size (N), edge number (E), clustering coefficient () and average shortest path length (). We consider seven recovery methods: degree recovery (DR), betweenness recovery (BR), local betweenness recovery (LBR), k-shell recovery (KR), random recovery (RR), greedy recovery (GR), hybrid recovery (HR).

学院论坛       会议室查询

北京师范大学系统科学学院  版权所有
邮箱:sss@bnu.edu.cn  邮编:100875  地址:北京市海淀区新街口外大街19号  电话:58804138

  • 微信
  • 科普