In this paper, we found the Moore-Penrose generalized inverse of adjacency matrix of an undirected graph, explicitly. We proved that the matrix $R_λ= [r_{ij}]$ is nonsingular where $r_{ii}=\frac{1}λ+ °v_i$ and $r_{ij}=\mid N_G(V_i)\cap N_G(V_j)\mid$ for $i\neq j$, and we proved that $A^{\dagger}_G=[s_{ij}]_{1\leq i, j \leq n}$ where $\displaystyle{s_{ij}=s_{ji}=\lim_{λ\rightarrow +\infty} \langle R^{-1}_λe_j, f_i \rangle }$. The proof of the main result was based on the Tikhonov regularization.