  In this paper, we establish Buser type inequalities, i.e., upper bounds for
eigenvalues in terms of Cheeger constants. We prove the Buser's inequality for
an infinite but locally finite connected graph with Ricci curvature lower
bounds. Furthermore, we derive that the graph with positive curvature is
finite, especially for unbounded Laplacians. By proving Poincar\'e inequality,
we obtain a lower bound on Cheeger constant in terms of positive curvature.
