Abstract: The Internet topology at router level is less focused on now. So, the massive data acquired in the period from January to December in 2006 and authorized by CAIDA Skitter project were used to analyze the searched topological data at CAIDA(cooperative association for Internet data analysis) router level, thus describing the characteristics of the distribution of the degrees of nodes at router level. Then, the core number for all nodes are computed, which embodies further the topological levels in Internet, thus describing the distribution of power laws of nodal cores especially the relationship between the degree and core number of nodes. It is revealed that the degree distribution relates to the power law for the nodes of low core number.