  The ever-increasing knowledge of the structure of various real-world networks
has uncovered their complex multi-mechanism-governed evolution processes.
Therefore, a better understanding of the structure and evolution of these
networked complex systems requires us to describe such processes in a more
detailed and realistic manner. In this paper, we introduce a new type of
network growth rule which comprises addition and deletion of nodes, and propose
an evolving network model to investigate the effect of node deleting on network
structure. It is found that, with the introduction of node deleting, network
structure is significantly transformed. In particular, degree distribution of
the network undergoes a transition from scale-free to exponential forms as the
intensity of node deleting increases. At the same time, nontrivial
disassortative degree correlation develops spontaneously as a natural result of
network evolution in the model. We also demonstrate that node deleting
introduced in the model does not destroy the connectedness of a growing network
so long as the increasing rate of edges is not excessively small. In addition,
it is found that node deleting will weaken but not eliminate the small-world
effect of a growing network, and generally it will decrease the clustering
coefficient in a network.
