  By extending a dynamical mean-field approximation (DMA) previously proposed
by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 41903 (2003)], we have
developed a semianalytical theory which takes into account a wide range of
couplings in a small-world network. Our network consists of noisy $N$-unit
FitzHugh-Nagumo (FN) neurons with couplings whose average coordination number
$Z$ may change from local ($Z \ll N $) to global couplings ($Z=N-1$) and/or
whose concentration of random couplings $p$ is allowed to vary from regular
($p=0$) to completely random (p=1). We have taken into account three kinds of
spatial correlations: the on-site correlation, the correlation for a coupled
pair and that for a pair without direct couplings. The original $2
N$-dimensional {\it stochastic} differential equations are transformed to
13-dimensional {\it deterministic} differential equations expressed in terms of
means, variances and covariances of state variables. The synchronization ratio
and the firing-time precision for an applied single spike have been discussed
as functions of $Z$ and $p$. Our calculations have shown that with increasing
$p$, the synchronization is {\it worse} because of increased heterogeneous
couplings, although the average network distance becomes shorter. Results
calculated by out theory are in good agreement with those by direct
simulations.
