Exploring self-similarity of complex cellular networks: The edge-covering method with simulated annealing and log-periodic sampling

Simple item page
dc.creatorZhou, Wei-Xing
dc.creatorJiang, Zhi-Qiang
dc.creatorSornette, Didier
dc.date2006-05-27
dc.date.accessioned2026-07-07T07:35:26Z
dc.date.available2026-07-07T07:35:26Z
dc.descriptionSong, Havlin and Makse (2005) have recently used a version of the box-counting method, called the node-covering method, to quantify the self-similar properties of 43 cellular networks: the minimal number $N_V$ of boxes of size $\ell$ needed to cover all the nodes of a cellular network was found to scale as the power law $N_V \sim (\ell+1)^{-D_V}$ with a fractal dimension $D_V=3.53\pm0.26$. We propose a new box-counting method based on edge-covering, which outperforms the node-covering approach when applied to strictly self-similar model networks, such as the Sierpinski network. The minimal number $N_E$ of boxes of size $\ell$ in the edge-covering method is obtained with the simulated annealing algorithm. We take into account the possible discrete scale symmetry of networks (artifactual and/or real), which is visualized in terms of log-periodic oscillations in the dependence of the logarithm of $N_E$ as a function of the logarithm of $\ell$. In this way, we are able to remove the bias of the estimator of the fractal dimension, existing for finite networks. With this new methodology, we find that $N_E$ scales with respect to $\ell$ as a power law $N_E \sim \ell^{-D_E}$ with $D_E=2.67\pm0.15$ for the 43 cellular networks previously analyzed by Song, Havlin and Makse (2005). Bootstrap tests suggest that the analyzed cellular networks may have a significant log-periodicity qualifying a discrete hierarchy with a scaling ratio close to 2. In sum, we propose that our method of edge-covering with simulated annealing and log-periodic sampling minimizes the significant bias in the determination of fractal dimensions in log-log regressions.
dc.description19 elsart pages including 9 eps figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0605676
dc.identifierhttp://arxiv.org/abs/cond-mat/0605676
dc.identifierPhysica A 375, 741-752 (2007)
dc.identifierdoi:10.1016/j.physa.2006.10.025
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120095
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.titleExploring self-similarity of complex cellular networks: The edge-covering method with simulated annealing and log-periodic sampling
dc.typetext

Files

Collections

arXiv