Hierarchical, Regular Small-World Networks
| dc.creator | Boettcher, S. | |
| dc.creator | Goncalves, B. | |
| dc.creator | Guclu, H. | |
| dc.date | 2007-12-08 | |
| dc.date | 2008-05-29 | |
| dc.date.accessioned | 2026-07-07T09:41:11Z | |
| dc.date.available | 2026-07-07T09:41:11Z | |
| dc.description | Two new classes of networks are introduced that resemble small-world properties. These networks are recursively constructed but retain a fixed, regular degree. They consist of a one-dimensional lattice backbone overlayed by a hierarchical sequence of long-distance links. Both types of networks, one 3-regular and the other 4-regular, lead to distinct behaviors, as revealed by renormalization group studies. The 3-regular networks are planar, have a diameter growing as \sqrt{N} with the system size N, and lead to super-diffusion with an exact, anomalous exponent d_w=1.3057581..., but possesses only a trivial fixed point T_c=0 for the Ising ferromagnet. In turn, the 4-regular networks are non-planar, have a diameter growing as ~2^[\sqrt(\log_2 N^2)], exhibit "ballistic" diffusion (d_w=1), and a non-trivial ferromagnetic transition, T_c>0. It suggest that the 3-regular networks are still quite "geometric", while the 4-regular networks qualify as true small-world networks with mean-field properties. As an example of an application we discuss synchronization of processors on these networks. | |
| dc.description | 9 pages, final version for JPA FastTrack, find related articles at http://www.physics.emory.edu/faculty/boettcher | |
| dc.identifier | https://arxiv.org/abs/0712.1259 | |
| dc.identifier | http://arxiv.org/abs/0712.1259 | |
| dc.identifier | J. Phys. A: Math. Theor. 41, 252001 (2008) | |
| dc.identifier | doi:10.1088/1751-8113/41/25/252001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161742 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Hierarchical, Regular Small-World Networks | |
| dc.type | text |