  Fast cortical rhythms with stochastic and intermittent neural discharges have
been observed in electric recordings of brain activity. Recently, Brunel et al.
developed a framework to describe this kind of fast sparse synchronization in
both random and globally-coupled networks of suprathreshold spiking neurons.
However, in a real cortical circuit, synaptic connections are known to have
complex topology which is neither regular nor random. Hence, in order to extend
the works of Brunel et al. to realistic neural networks, we study the effect of
network architecture on these fast sparsely synchronized rhythms in an
inhibitory population of suprathreshold fast spiking (FS) Izhikevich
interneurons. We first employ the conventional Erd\"{o}s-Renyi random graph of
suprathreshold FS Izhikevich interneurons for modeling the complex connectivity
in neural systems, and study emergence of the population synchronized states by
varying both the synaptic inhibition strength $J$ and the noise intensity $D$.
Thus, fast sparsely synchronized states of relatively high degree are found to
appear for large values of $J$ and $D$. Second, for fixed values of $J$ and $D$
where fast sparse synchronization occurs in the random network, we consider the
Watts-Strogatz small-world network of suprathreshold FS Izhikevich interneurons
which interpolates between regular lattice and random graph via rewiring, and
investigate the effect of small-world synaptic connectivity on emergence of
fast sparsely synchronized rhythms by varying the rewiring probability $p$ from
short-range to long-range connection. When passing a small critical value
$p^*_c$ $(\simeq 0.12)$, fast sparsely synchronized population rhythms are
found to emerge in small-world networks with predominantly local connections
and rare long-range connections.
