  Information of localization properties of eigenvectors of the complex network
has applicability in many different areas which include networks centrality
measures, spectral partitioning, development of approximation algorithms, and
disease spreading phenomenon. For linear dynamical process localization of
principal eigenvector (PEV) of adjacency matrices infers condensation of the
information in the smaller section of the network. For a network, an
eigenvector is said to be localized when most of its components are near to
zero with few taking very high values. Here, we provide three different
random-sampling-based algorithms which, by using the edge rewiring method, can
evolve a random network having a delocalized PEV to a network having a highly
localized PEV. In other words, we develop a learning framework to explore the
localization of PEV through a random sampling-based optimization method. We
discuss the drawbacks and advantages of these algorithms. Additionally, we show
that the construction of such networks corresponding to the highly localized
PEV is a non-convex optimization problem when the objective function is the
inverse participation ratio. This framework is also relevant to construct a
network structure for other lower-order eigenvectors.
