Spectral similarity for Barabási-Albert and Chung-Lu models

Abstract: In the paper we have analyzed spectral similarity between Barab\'asi-Albert and Chung-lu models. We have shown the similarity of spectral distribution for sufficiently large Barab\'asi-Albert parameter value. Contrary, extreme eigenvalues and principal eigenvector are not similar for those model. We provide applications of obtained results related to the spectral graph theory and efficiency of quantum spatial search