  For modeling complex synaptic connectivity, we consider the Watts-Strogatz
small-world network which interpolates between regular lattice and random
network via rewiring, and investigate the effect of small-world connectivity on
emergence of noise-induced population synchronization in an inhibitory
population of subthreshold bursting Hindmarsh-Rose neurons. Thus, noise-induced
slow burst synchronization and fasg spike synchronization are found to appear
in a synchronized region of the $J-D$ plane. As the rewiring probability $p$ is
decreased from 1 (random network) to 0 (regular lattice), the region of spike
synchronization shrinks rapidly in the $J-D$ plane, while the region of the
burst synchronization decreases slowly. Population synchronization may be well
visualized in the raster plot of neural spikes which can be obtained in
experiments. Instantaneous population firing rate, $R(t)$, which is directly
obtained from the raster plot of spikes, is a realistic population quantity
exhibiting collective behaviors with both the slow bursting and the fast
spiking timescales. Through frequency filtering, we separate $R(t)$ into
$R_b(t)$ (describing the slow bursting behavior) and $R_s(t)$ (describing the
fast intraburst spiking behavior). Then, we develop thermodynamic order
parameters and statistical-mechanical measures, based on $R_b (t)$ and $R_s
(t)$, for characterization of the burst and spike synchronizations of the
bursting neurons and show their usefulness in explicit examples. With increase
in $p$, both the degrees of the burst and spike synchronizations are found to
increase because more long-range connections appear. However, they become
saturated for some maximal values of $p$ because long-range short-cuts which
appear up to the maximal values of $p$ play sufficient role to get maximal
degrees of the burst and spike synchronizations.
