Network construction: A learning framework through localizing principal eigenvector

Recently, eigenvector localization of complex network has seen a spurt in activities due to its versatile applicability in many different areas which includes networks centrality measure, spectral partitioning, development of approximation algorithms and disease spreading phenomenon. 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 develop three different randomized algorithms, which by using edge rewiring method, can evolve a random network having a delocalized principal eigenvector to a network having a highly localized principal eigenvector. We discuss drawbacks and advantages of these algorithms. Additionally, we show that the construction of such networks corresponding to the highly localized principal eigenvector is a non-convex optimization problem when the objective function is the inverse participation ratio.