  In this paper we prove the semi-circular law for the eigenvalues of regular
random graph $G_{n,d}$ in the case $d\rightarrow \infty$, complementing a
previous result of McKay for fixed $d$. We also obtain a upper bound on the
infinity norm of eigenvectors of Erd\H{o}s-R\'enyi random graph $G(n,p)$,
answering a question raised by Dekel-Lee-Linial.
