Message authentication is considered as a serious bottleneck to multicast security, particular for stream-type of traffic. The technique of hash chaining/signature amortization has been proposed in many schemes for stream authentication, with or without multicast settings. However, none of them is optimal. They either have a large packet overhead or are not robust to packet loss. Some even have a large receiver delay or require a large receiver buffer size. These schemes are constructed by trial-and-error methods. There lack tools to evaluate and compare their performances. There is no systematic way to construct these schemes either. In this paper, we introduce the notion of dependence-graphs which links these hash-chained authentication schemes to the well-known graph theory, and provides an effective analytical tool. Many important metrics of a hash-chained authentication scheme can be readily and easily determined from its dependence-graph. As well, a dependence-graph demonstrates design tradeoff and provides insights into optimizing hash-chained schemes.