Multifractal analysis of eigenvectors of small-world networks

Many real-world complex systems have small-world topology characterized by the high clustering of nodes and short path lengths.It is well-known that higher drives localization while shorter length supports delocalization eigenvectors networks. Using multifractals technique, we investigate properties adjacency matrices networks constructed using Watts-Strogatz algorithm. We find central part eigenvalue spectrum strong multifractality whereas tail Dq->1. Before onset transition, an increase in random connections leads to enhancement localization, just after onset, show a gradual decrease localization. verified existence sharp change correlation dimension at localization-delocalization transition