Summary: In this paper we solve the problem of secure communication in multicast graphs, which has been open for over a decade. In [“Secure communication in minimal connectivity models”, Lect. Notes Comput. Sci. 1403, 346‒360 (1998; Zbl 0929.68055)], {\it M. K. Franklin} and {\it R. Wright} initiated the study of secure communication against a Byzantine adversary on multicast channels in a neighbor network setting. Their model requires node-disjoint and neighbor-disjoint paths between a sender and a receiver. This requirement is too strong and hence not necessary in the general multicast graph setting. The research to find the lower and upper bounds on network connectivity for secure communication in multicast graphs has been carried out ever since. However, up until this day, there is no tight bound found for any level of security. We study this problem from a new direction, i.e., we find the necessary and sufficient conditions (tight lower and upper bounds) for secure communication in the general adversary model with adversary structures, and then apply the results to the threshold model. Our solution uses an extended characterization of the multicast graphs, which is based on our observation on the eavesdropping and separating activities of the Byzantine adversary.