  In 1970s, Gutman introduced the concept of the energy $\En(G)$ for a simple
graph $G$, which is defined as the sum of the absolute values of the
eigenvalues of $G$. This graph invariant has attracted much attention, and many
lower and upper bounds have been established for some classes of graphs among
which bipartite graphs are of particular interest. But there are only a few
graphs attaining the equalities of those bounds. We however obtain an exact
estimate of the energy for almost all graphs by Wigner's semi-circle law, which
generalizes a result of Nikiforov. We further investigate the energy of random
multipartite graphs by considering a generalization of Wigner matrix, and
obtain some estimates of the energy for random multipartite graphs.
