  When analyzing the statistical and topological characteristics of complex
networks, an effective and convenient way is to compute the centralities for
recognizing influential and significant nodes or structures, yet most of them
are restricted to local environment or some specific configurations. In this
paper we propose a new centrality for nodes based on the von Neumann entropy,
which allows us to investigate the importance of nodes in the view of spectrum
eigenvalues distribution. By presenting the performances of this centrality
with network examples in reality, it is shown that the von Neumann entropy node
centrality is an excellent index for selecting crucial nodes as well as
classical ones. Then to lower down the computational complexity, an
approximation calculation to this centrality is given which only depends on its
first and second neighbors. Furthermore, in the optimal spreader problem and
reducing average clustering coefficients, this entropy centrality presents
excellent efficiency and unveil topological structure features of networks
accurately. The entropy centrality could reduce the scales of giant connected
components fastly in Erdos-Renyi and scale-free networks, and break down the
cluster structures efficiently in random geometric graphs. This new methodology
reveals the node importance in the perspective of spectrum, which provides a
new insight into networks research and performs great potentials to discover
essential structural features in networks.
