Traditionally, the Byzantine agreement (BA) problem has been studied either in a fully connected network or in a broadcast network. Here, a generalized network model for BA is proposed. The conventional fully connected network or broadcast network is a special case of the new network architecture. A BA problem with the processor in a malicious fault is studied in the model. The proposed protocol incorporates the previous protocols developed for a fully connected network or a broadcast network, solves a BA problem by using the minimum number of rounds, and can tolerate the maximum number of faulty processors.