In this paper, an innovative metric called Average Degree of Disconnectivity (Average DOD) is proposed. The Average DOD combining the concept of the probability calculated by contest success function with the DOD metric would be used to evaluate the damage degree of network. The larger value of the Average DOD, the more damage degree of the network would be. An attack-defense scenario as a mathematical model would be used to support network operators to predict that all the likelihood strategies both cyber attacker and network defender would take. The attacker could use the attack resources to launch attack on the nodes of network. On the other hand, the network defender allocates existed resources of defender to protect survival nodes of network. In the process of problem solving, the "gradient method" and "game theory" would be adopted to find the optimal resource allocation strategies for both cyber attacker and network defender.