Sample compression schemes were first proposed by Littlestone and Warmuth in 1986. Proper compression can guarantee good generalization performance. Undirected graphical model is a powerful tool for classification in machine learning. In this paper, we consider labeled compression schemes for concept classes induced by discrete undirected graphical models. For the undirected graph of two vertices with no edge, $X_{1} \in \{0,1\}$, $X_{2} \in \{0,1,\ldots,k_{2}-1\}$ ($k_{2} \in \mathbb{N}$, $k_{2} \ge 2$), we establish a labeled compression scheme of size $k_{2}+1$. Furthermore, we construct a labeled compression scheme of size VC dimension for classes associated the undirected graph which has three vertices ${X_1}$, ${X_2}$, ${X_3}$ and two edges, where $X_{1} \in \{0,1\}$, $X_{i} \in \{ {0,1,\ldots,k_{i} - 1}\}$, $k_{i} \in \mathbb{N}$, $k_{i} \ge 2$, $i=2,3$. Consequently, for any undirected graphical model whose underlying graph has two cliques $K_{1}=\{X_{1}, X_{2}, \ldots, X_{n_{1}}\}$, $K_{2}=\{X_{2}, X_{3}, \ldots, X_{n}\}$ with $X_{1}\in \{0,1\}$, there is a labeled compression scheme of size VC dimension of the corresponding concept class. It is an open question whether the concept class induced by a general discrete undirected graphical model has a sample compression scheme of size VC dimension.