Abstract
The capacity factor, as a useful tool, was used to characterize the dependence of every link on the capacity changes of a network coding based network. In this paper, we shall investigate the relationship between the network capacity and the set of capacity factors. We firstly introduce a new concept, the capacity kernel, which is a subnetwork deduced from the original network. It will be shown that the capacity kernel of a network maintains most important capacity-related properties of the original network. The capacity kernel can also deduce a projection operator, which to the best of our knowledge, is the first known projection operator acting on the space of all the communication networks. We further introduce and discuss the properties of the C-contra links based on the capacity kernel. As an application, a tighter upper bound on the capacity factor size is then obtained.