  Identifying the most influential spreaders is an important issue in
understanding and controlling spreading processes on complex networks. Recent
studies showed that nodes located in the core of a network as identified by the
k-shell decomposition are the most influential spreaders. However, through a
great deal of numerical simulations, we observe that not in all real networks
do nodes in high shells are very influential: in some networks the core nodes
are the most influential which we call true core, while in others nodes in high
shells, even the innermost core, are not good spreaders which we call core-like
group. By analyzing the k-core structure of the networks, we find that the true
core of a network links diversely to the shells of the network, while the
core-like group links very locally within the group. For nodes in the core-like
group, the k-shell index cannot reflect their location importance in the
network. We further introduce a measure based on the link diversity of shells
to effectively distinguish the true core and core-like group, and identify
core-like groups throughout the networks. Our findings help to better
understand the structural features of real networks and influential nodes.
