Network coding encourages information flow mixing in a network. It helps increase the throughput and reduce the cost of data transmission, especially for one-to-many multicast applications. An interesting problem is to understand and quantify the coding advantage and cost advantage, the potential benefits of network coding, as compared to routing, in terms of increasing throughput and reducing transmission cost, respectively. Two classic network models were considered in previous studies: directed networks and undirected networks. This paper further focuses on two types of parameterized networks, including bi-directed networks and hyper networks, generalizing the directed and the undirected network models, respectively.