Security of the key host is of prime importance to the overall network, but locating the key host
difficult. This paper gives a definition of key hosts, provides their classification, and propose an approach to
finding the key hosts. The method uses the host-based attack graph and the theory of iterative matrix. By
computing and sorting the security properties of each host, the network security administrator can identify
key hosts and the corresponding key critical-conditions. Appropriate measures can then be taken to protect
the key hosts and enhance the overall network security. Experiment shows that this approach can be applied
to the analysis of network security, and is useful for the enhancement of network security.