Controlling centrality: The inverse ranking problem for spectral centralities of complex networks

In this paper, some results about the controllability of spectral centrality in a complex network are presented. particular, inverse problem designing an unweigthed graph with prescribed is considered. We show that for every possible ranking, eventually ties, unweighted directed/undirected can be found whose PageRank or eigenvector gives ranking Different families networks presented order to analytically solve either directed and undirected graphs without loops.