摘要
度量网络节点(集)的重要性一直是社会网络分析领域和系统科学研究领域的一个值得研究的问题。系统科学的研究方法用网络的连通性来反映系统某种功能的完整性,通过度量节点删除对网络连通的破坏程度来反映网络节点(集)的重要性,但目前这一思想并没有得到真正意义上的量化,如果不考虑连通分支的大小和形状,就不能很好地反映出不同节点或不同网络之间在结构和位置特性上的差异。本文用节点(集)被删除后形成的所有不连通节点对之间的距离(最短路)的倒数之和来反应节点删除对网络连通的破坏程度即所删节点(集)的重要性。这一工作使重要性等价于破坏性的思想得到了精细的量化。
It has been a valuable research topic to measure the importance of an actor (set) within a network in the fields of both social network analysis and system science. Most of the measures in social network analysis focused on enlarging the differences among the actors embedded in a network for some attributes of connections among the actors,so as to differenti- ate the importance of different actors. In system science research, connectivity is used to characterize the integrality of a system function, the importance of an actor (set) within a network is characterized as the extent to which the network has been destroyed by deleting an actor (set) (Xu,Xi and Wang,1993). But up to now, this notion has not been quantified in real meaning. It is impossible for us to provide a better description to the differences in structure and position property of different actors or networks unless the size and form of connected components resulted from deleting an actor (set) are taken into account. This paper use the sum of reciprocal of all geodesics between a pair of disconnected actors caused by deleting an actor (set) to characterize the extent to which the network has been destroyed, i.e. the importance index of deleting an actor (set). The notion of equaling importance to endangerment (Xu,Xi and Wang,1993; Xi & Tang,2002) has been nicely quantified in this work.
出处
《系统工程》
CSCD
北大核心
2004年第4期13-20,共8页
Systems Engineering
基金
国家自然科学基金优秀创新研究群体基金资助项目(7012001)
国家自然科学基金资助项目(70202003)
