  Identifying the most influential spreaders is an important issue in
controlling the spreading processes in complex networks. Centrality measures
are used to rank node influence in a spreading dynamics. Here we propose a node
influence measure based on the centrality of a node and its neighbors'
centrality, which we call the neighborhood centrality. By simulating the
spreading processes in six real-world networks, we find that the neighborhood
centrality greatly outperforms the basic centrality of a node such as the
degree and coreness in ranking node influence and identifying the most
influential spreaders. Interestingly, we discover a saturation effect in
considering the neighborhood of a node, which is not the case of the larger the
better. Specifically speaking, considering the 2-step neighborhood of nodes is
a good choice that balances the cost and performance. If further step of
neighborhood is taken into consideration, there is no obvious improvement and
even decrease in the ranking performance. The saturation effect may be
informative for studies that make use of the local structure of a node to
determine its importance in the network.
