title: Full eigenvalues of the Markov matrix for scale-free polymer networks.
abstract: Much important information about the structural and dynamical properties of complex systems can be extracted from the eigenvalues and eigenvectors of a Markov matrix associated with random walks performed on these systems, and spectral methods have become an indispensable tool in the complex system analysis. In this paper, we study the Markov matrix of a class of scale-free polymer networks. We present an exact analytical expression for all the eigenvalues and determine explicitly their multiplicities. We then use the obtained eigenvalues to derive an explicit formula for the random target access time for random walks on the studied networks. Furthermore, based on the link between the eigenvalues of the Markov matrix and the number of spanning trees, we confirm the validity of the obtained eigenvalues and their corresponding degeneracies.
authors.affiliation: School of Computer Science and Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Zhongzhi
authors.initials: Z
authors.lastname: Zhang
authors.affiliation: School of Computer Science and Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Xiaoye
authors.initials: X
authors.lastname: Guo
authors.affiliation: School of Computer Science and Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Lin
mesh_terms: D008962:Models, Theoretical; D011108:Polymers
chemical_list: D011108:Polymers