| Recent years, many works have tried to study geometrical statistics of real-world networks from complex networks views. The results show that many real networks have similar characteristics, such as small word, power-law distributions and the high clustering and so on. Topology of networks is a hot topic in research of complex networks.The studies along this line have been able to model, investigate certain dynamical problems on network topologies and study how the geometric characteristics and performances of the networks are affected by the restrictions imposed on networks.Scale-free property has been found both in nature systems and real-world systems. It has shown the difference between degrees of network nodes. In a certain network, there are always some nodes which take an important role in the whole network topologies. These nodes take important effects on the traffic of network flows. If these nodes happen to block or have been attacked, it will influence the haleness, stability and efficiency of the networks as much as the paralysis of the whole or part of network.In order to determine the importance of nodes, this paper constructs kernel subnet using the concept of dominating sets in graphics theory. This kernel subnet sets up the relation of microcosmic characteristics and the whole magnificent properties of networks, and demonstrates the topological comparability between the kernel subnets and the original networks.In this paper, we measured the statistic property of kernel subnets using the distributions of node degrees, and discovered that the kernel subnets have the scale-free property as the same as the original networks. Finally, this paper analysis the changes of connection fraction in original networks, when kernel subnets take errors or attacked. |
