In this paper, we prove the following: Let G be a graph, f:G->G a continuous map and P a finite subset of G such that f(P) P. Then there exist a regular continuum Z, a continuous map g:Z->Z and a semi-conjugacy π:G->Z such that(1) g is π(P)-expansive, and(2) if p,q P and Q is a subset of P with A Q<> for any arc A in G between p and q, then A' π(Q)<> for any arc A' in Z between π(p) and π(q).In addition, f is point-wise P-expansive if and only if π P is one-to-one.In this paper we are especially interested in the geometrical structure of Z. Actually we can see the complicated construction of Z.