added to the given index coding instance, where $\mathcal{G}$ becomes $\mathcal{G}^{\prime}$ and $\bm{\delta}_s$ becomes $\bm{\delta}_s^{\prime}$.

For simplicity, we can assume that every receiver wants to receive only one message because a receiver who wants to receive more than one message can be split into receivers with identical side information. Now, we explain how to make $\mathcal{G}^{\prime}$, $\bm{\delta}_s^{\prime}$, and the corresponding network coding instance including $\mathbb{G}$ and $\bm{\delta}$.

In order to make the corresponding network coding instance using the same relationship between two coding instances in the previous section, it is necessary to determine which part is $\bold{\hat{X}}_E$ or $\bold{\hat{X}}_S$ for a given side information graph $\mathcal{G}$. $\hat{X}_e$ is said to be a unicast message if $\hat{X}_e$ is wanted by one receiver. Suppose that the maximal unicast acyclic subgraph of $\mathcal{G}$ consists of unicast messages $\bold{\hat{X}}_{E}$ and the receivers who want one of $\bold{\hat{X}}_{E}$, that is, $\{R_{e} | e\in E\}$. In such a case, the validity of the corresponding network structure is not guaranteed but for the directed acyclic network structure, it is guaranteed when we convert $\mathcal{G}$ to the corresponding network structure as in the previous section. Next, let $\bold{\hat{X}}_S$ and $\{R_t | t\in T\}$ be the remaining messages and 