  Energy level statistics of Hermitian random matrices $\hat H$ with Gaussian
independent random entries $H_{i\geq j}$ is studied for a generic ensemble of
almost diagonal random matrices with $ <|H_{ii}|^{2} > \sim 1$ and $<|H_{i\neq
j}|^{2} >= b {\cal F}(|i-j|) \ll 1$. We perform a regular expansion of the
spectral form-factor $K(\tau) = 1 + b K_{1}(\tau) + b^{2} K_{2}(\tau) + ... $
in powers of $b \ll 1$ with the coefficients $K_{m}(\tau)$ that take into
account interaction of (m+1) energy levels. To calculate $K_{m}(\tau)$, we
develop a diagrammatic technique which is based on the Trotter formula and on
the combinatorial problem of graph edges coloring with (m+1) colors.
Expressions for $K_{1}(\tau)$ and $K_{2}(\tau)$ in terms of infinite series are
found for a generic function ${\cal F}(|i-j|)$ in the Gaussian Orthogonal
Ensemble (GOE), the Gaussian Unitary Ensemble (GUE) and in the crossover
between them (the almost unitary Gaussian ensemble). The Rosenzweig-Porter and
power-law banded matrix ensembles are considered as examples.
