  We study the evolution of networks when the creation and decay of links are
based on the position of nodes in the network measured by their centrality. We
show that the same network dynamics arises under various centrality measures,
and solve analytically the network evolution. During the complete evolution,
the network is characterized by nestedness: the neighbourhood of a node is
contained in the neighbourhood of the nodes with larger degree. We find a
discontinuous transition in the network density between hierarchical and
homogeneous networks, depending on the rate of link decay. We also show that
this evolution mechanism leads to double power-law degree distributions, with
interrelated exponents.
