Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-06-21
Physics
Condensed Matter
Statistical Mechanics
10 pages, 3 figures
Scientific paper
The spectral dimension has been widely used to understand transport properties on regular and fractal lattices. Nevertheless, it has been little studied for complex networks such as scale-free and small world networks. Here we study the spectral dimension and the return-to-origin probability of random walks on hierarchical scale-free networks, which can be either fractals or non-fractals depending on the weight of shortcuts. Applying the renormalization group (RG) approach to the Gaussian model, we obtain the spectral dimension exactly. While the spectral dimension varies between $1$ and $2$ for the fractal case, it remains at $2$, independent of the variation of network structure for the non-fractal case. The crossover behavior between the two cases is studied through the RG flow analysis. The analytic results are confirmed by simulation results and their implications for the architecture of complex systems are discussed.
Hwang Seungsu
Kahng Byungnam
Kim Dongseok
Lee Da-Shin
Yun C.-K.
No associations
LandOfFree
Spectral dimensions of hierarchical scale-free networks with shortcuts does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Spectral dimensions of hierarchical scale-free networks with shortcuts, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral dimensions of hierarchical scale-free networks with shortcuts will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-600903