In this paper, the correspondence between the weighted line graph and the Mason signal flow graph (MSFG) has been established, which gives an interpretation of a convolutional network code (CNC) over a cyclic network from a different perspective. Furthermore, by virtue of Mason theorem, we present two new equivalent conditions to evaluate whether the global encoding kernels (GEKs) can be uniquely determined by the given complete set of local encoding kernels (LEKs) in a CNC over a cyclic network. These two new equivalent conditions turn out to be more intuitive. Moreover, we give an alternative simple proof of an existing result.