节点被删除后的复杂网络子集团数量研究

Research on the Sub-Group Number upon the Deletion of Complex Network Nodes

现实当中的许多复杂网络都无法避免地受到来自自然灾害或人为的攻击,从而导致网络破碎成很多大大小小的子集团.计算随机网络和BA无标度网络在随机删除节点与蓄意删除节点两种情况下产生的除最大连通图外其他子集团数量的情况.在产生的子集团中,结果发现它们特点是当节点删除比例f从0增大到1过程中,子集团的数量先增大后减小.包含节点数量较小的子集团数量占子集团总数量的大多数.子集团尺寸与相应数量在尺寸较小时近似成幂律关系.随机与蓄意删除节点时,随机网络与BA无标度网络产生子集团数量的最大值存在差异.

Many complex networks are vulnerable to the attacks from natural disasters or human interference and are broken into many big and small sub-groups. This study addresses the num-ber of the sub-groups, with the exception of the largest connected cluster, produced by the ran-dom network and the BA scale-free network respectively in the cases of random and deliberate deletion of nodes. The result shows that, when the deletion percentage of nodes increases from 0 to 1, the number of sub-groups increases first and then decreases. The number of the sub-groups that contains a small number of nodes accounts for the majority of the total number of sub-groups. Sub-group size and its corresponding number approximate power-law relationship when the size is smaller. Differences between the max values of the sub-groups produced by the random network and the BA scale-free network are found when nodes are randomly and deliber-ately deleted.