  In pinning control of complex networks, a tacit believing is that the system
dynamics will be better controlled by pinning the large-degree nodes than the
small-degree ones. Here, by changing the number of pinned nodes, we find that,
when a significant fraction of the network nodes are pinned, pinning the
small-degree nodes could generally have a higher performance than pinning the
large-degree nodes. We demonstrate this interesting phenomenon on a variety of
complex networks, and analyze the underlying mechanisms by the model of star
networks. By changing the network properties, we also find that, comparing to
densely connected homogeneous networks, the advantage of the small-degree
pinning strategy is more distinct in sparsely connected heterogenous networks.
