Exact eigenvalue spectrum of a class of fractal scale-free networks
arXiv:1207.1546 · doi:10.1209/0295-5075/99/10007
Abstract
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine all the eigenvalues and their degeneracies. We then use these eigenvalues to evaluate the closed-form solution to the eigentime for random walks on the networks under consideration. Through the connection between the spectrum of transition matrix and the number of spanning trees, we corroborate the obtained eigenvalues and their multiplicities.
arXiv commentDefinitive version accepted for publication in EPL (Europhysics Letters)
References in corpus (28)
- Emergence of scaling in random networks
- Statistical mechanics of complex networks
- The structure and function of complex networks
- Evolution of networks
- Critical phenomena in complex networks
- Self-similarity of complex networks
- Intermittent search strategies
- Network Physiology reveals relations between network topology and physiological function
- First-passage times in complex scale-invariant media
- Origins of fractality in the growth of complex networks
- Spectra of complex networks
- Scaling theory of transport in complex networks
- Fractal and Transfractal Recursive Scale-Free Nets
- Global mean first-passage times of random walks on complex networks
- Biased random walks on complex networks: the role of local navigation rules
- First Passage Properties of the Erdos-Renyi Random Graph
- Percolation in Hierarchical Scale-Free Nets
- Determining global mean-first-passage time of random walks on Vicsek fractals using eigenvalues of Laplacian matrices
- Mean first-passage time for random walks on undirected networks
- Pascal Principle for Diffusion-Controlled Trapping Reactions
- Spectral dimensions of hierarchical scale-free networks with shortcuts
- Trapping in complex networks
- Lattice theory of trapping reactions with mobile species
- Counting spanning trees in a small-world Farey graph
- Close or connected? Distance and connectivity effects on transport in networks
- Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics
- Counting spanning trees in self-similar networks by evaluating determinants
- Transition from fractal to non-fractal scalings in growing scale-free networks