  In this paper, we defined three kinds of measures depending on the given
finite directed graphs. For the given finite directed graph, we can construct
the free semigroupoid, the diagram set and the reduced diagram set, as
algebraic structures determined by the admissibility on the graph. The power
sets of such structures are sigma algebras of them, respectively. On them, we
can define a measure. The pain purpose of this paper is to introduce those
three measures and observe some properties of them. Moreover, we consider
Measure Theory on them
