Fractality in complex networks: critical and supercritical skeletons
| dc.creator | Kim, J. S. | |
| dc.creator | Goh, K. -I. | |
| dc.creator | Salvi, G. | |
| dc.creator | Oh, E. | |
| dc.creator | Kahng, B. | |
| dc.creator | Kim, D. | |
| dc.date | 2006-05-12 | |
| dc.date.accessioned | 2026-07-07T09:35:39Z | |
| dc.date.available | 2026-07-07T09:35:39Z | |
| dc.description | Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a new box-covering algorithm that is a modified version of the original algorithm introduced by Song et al. [Nature (London) 433, 392 (2005)]; this algorithm enables effective computation and easy implementation. Fractal networks are viewed as comprising a skeleton and shortcuts. The skeleton, embedded underneath the original network, is a special type of spanning tree based on the edge betweenness centrality; it provides a scaffold for the fractality of the network. When the skeleton is regarded as a branching tree, it exhibits a plateau in the mean branching number as a function of the distance from a root. Based on these observations, we construct a fractal network model by combining a random branching tree and local shortcuts. The scaffold branching tree can be either critical or supercritical, depending on the small-worldness of a given network. For the network constructed from the critical (supercritical) branching tree, the average number of vertices within a given box grows with the lateral size of the box according to a power-law (an exponential) form in the cluster-growing method. The distribution of box masses, i.e., the number of vertices within each box, follows a power law P_m(M) sim M^{-eta}. The exponent eta depends on the box lateral size ell_B. For small values of ell_B, eta is equal to the degree exponent gamma of a given scale-free network, whereas eta approaches the exponent tau=gamma/(gamma-1) as ell_B increases, which is the exponent of the cluster-size distribution of the random branching tree. We also study the perimeter of a given box as a function of the box mass. | |
| dc.description | 14 pages, 18 figures, 2 tables | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0605324 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0605324 | |
| dc.identifier | Phys. Rev. E 75, 016110 (2007). | |
| dc.identifier | doi:10.1103/PhysRevE.75.016110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159903 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Fractality in complex networks: critical and supercritical skeletons | |
| dc.type | text |