  In this paper, we found the Moore-Penrose generalized inverse of adjacency
matrix of an undirected graph, explicitly. We proved that the matrix
$R_\lambda= [r_{ij}]$ is nonsingular where $r_{ii}=\frac{1}{\lambda}+ \deg v_i$
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
$\displaystyle{s_{ij}=s_{ji}=\lim_{\lambda \rightarrow +\infty} \langle
R^{-1}_{\lambda}e_j, f_i \rangle }$. The proof of the main result was based on
the Tikhonov regularization.
