  We investigate the effect of network architecture on burst and spike
synchronization in a directed scale-free network (SFN) of bursting neurons,
evolved via two independent $\alpha-$ and $\beta-$processes. The
$\alpha-$process corresponds to a directed version of the Barab\'{a}si-Albert
SFN model with growth and preferential attachment, while for the
$\beta-$process only preferential attachments between pre-existing nodes are
made without addition of new nodes. We first consider the "pure"
$\alpha-$process of symmetric preferential attachment (with the same in- and
out-degrees), and study emergence of burst and spike synchronization by varying
the coupling strength $J$ and the noise intensity $D$ for a fixed attachment
degree. Characterizations of burst and spike synchronization are also made by
employing realistic order parameters and statistical-mechanical measures. Next,
we choose appropriate values of $J$ and $D$ where only the burst
synchronization occurs, and investigate the effect of the scale-free
connectivity on the burst synchronization by varying (1) the symmetric
attachment degree and (2) the asymmetry parameter (representing deviation from
the symmetric case) in the $\alpha-$process, and (3) the occurrence probability
of the $\beta-$process. In all these three cases, changes in the type and the
degree of population synchronization are studied in connection with the network
topology such as the degree distribution, the average path length $L_p$, and
the betweenness centralization $B_c$. It is thus found that not only $L_p$ and
$B_c$ (affecting global communication between nodes) but also the in-degree
distribution (affecting individual dynamics) are important network factors for
effective population synchronization in SFNs.
