On the α-nonbacktracking centrality for complex networks: Existence and limit cases

Nonbactracking centrality was introduced as an attempt to correct some deficiencies of eigenvector centrality. In this work the α-nonbacktracking centrality is introduced as an extension that interpolates between the nonbacktracking centrality of the edges of a directed network and the eigenvector centrality of the corresponding directed line graph. The existence of this new α-nonbacktracking centrality is proved in terms of the connectivity of the original network.