  A graph state and a graph code respectively are defined based on a
mathematical simple graph. In this work, we examine a relation between a graph
state and a graph code both obtained from the same graph, and show that a graph
state is a superposition of logical qubits of the related graph code. By using
the relation, we first discuss that a local complementation which has been used
for a graph state can be useful for searching locally equivalent stabilizer
codes, and second provide a method to find a stabilizer group of a graph code.
