  Investigation of eigenvector localization properties of complex networks is
not only important for gaining insight into fundamental network problems such
as network centrality measure, spectral partitioning, development of
approximation algorithms, but also is crucial for understanding many real-world
phenomena such as disease spreading, criticality in brain network dynamics. For
a network, an eigenvector is said to be localized when most of its components
take value near to zero, with a few components taking very high values. In this
article, we devise a methodology to construct a principal eigenvector (PEV)
localized network from a given input network. The methodology relies on adding
a small component having a wheel graph to the given input network. By extensive
numerical simulation and an analytical formulation based on the largest
eigenvalue of the input network, we compute the size of the wheel graph
required to localize the PEV of the combined network. Using the
susceptible-infected-susceptible model, we demonstrate the success of this
method for various models and real-world networks consider as input networks.
We show that on such PEV localized networks, the disease gets localized within
a small region of the network structure before the outbreaks. The study is
relevant in controlling spreading processes on complex systems represented by
networks.
