Most practical networks are cyclic and demand Convolutional network coding(CNC). Researches on application of CNC in practical networks are still insufficient. Conventional graph theories cannot model the multicast channel properly. This paper introduces a multicast graph with multicast edges to model the multicast networks, and proposes a Multicast edge generation and max-flow detection(MEGAMAD) algorithm to approach the lower bound of necessary multicast edge number for a multicast network. Based on the algorithm we designed a new Media access control(MAC) protocol, the CNC oriented four-stage contention protocol(NC-FSCP) for the all-to-all broadcasting networks. The protocol runs a four stage reservation procedure to reserve time slots for encoded data transmission. Simulation proves that the reserved slot number approaches the lower bound for data dispersion in an all-to-all broadcasting network. Most practical networks are cyclic and demand Convolutional network coding (CNC). Researches on application of CNC in practical networks are still insufficient. Conventional graphologies can not model the multicast channel properly. This paper introduces a multicast graph with multicast edges to model the multicast networks , and proposes a Multicast edge generation and max-flow detection (MEGAMAD) algorithm to approach the lower bound of necessary multicast edge number for a multicast network. Based on the algorithm we designed a new Media access control (MAC) protocol, the CNC oriented Four-stage contention protocol (NC-FSCP) for the all-to-all broadcasting networks. The protocol runs a four stage reservation procedure to reserve time slots for encoded data transmission. Simulation proves that the reserved slot number approaches the lower bound for data dispersion in an all-to-all broadcasting network.