title: Spectra of weighted scale-free networks.
abstract: Much information about the structure and dynamics of a network is encoded in the eigenvalues of its transition matrix. In this paper, we present a first study on the transition matrix of a family of weight driven networks, whose degree, strength, and edge weight obey power-law distributions, as observed in diverse real networks. We analytically obtain all the eigenvalues, as well as their multiplicities. We then apply the obtained eigenvalues to derive a closed-form expression for the random target access time for biased random walks occurring on the studied weighted networks. Moreover, using the connection between the eigenvalues of the transition matrix of a network and its weighted spanning trees, we validate the obtained eigenvalues and their multiplicities. We show that the power-law weight distribution has a strong effect on the behavior of random walks.
authors.affiliation: School of Computer Science, Fudan University, Shanghai 200433, China.|Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Zhongzhi
authors.initials: Z
authors.lastname: Zhang
authors.affiliation: School of Computer Science, Fudan University, Shanghai 200433, China.|Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Xiaoye
authors.initials: X
authors.lastname: Guo
authors.affiliation: School of Computer Science, Fudan University, Shanghai 200433, China.|Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
authors.forename: Yuhao
authors.initials: Y
authors.lastname: Yi