Scalefree network topology and multifractality in a weighted planar stochastic lattice
Abstract
We propose a weighted planar stochastic lattice (WPSL) formed by the random sequential partition of a plane into contiguous and nonoverlapping blocks and we find that it evolves following several nontrivial conservation laws, namely \sum_i^N x_i^{n1} y_i^{4/n1} is independent of time ∀n, where x_{i} and y_{i} are the length and width of the ith block. Its dual on the other hand, obtained by replacing each block with a node at its centre and the common border between blocks with an edge joining the two vertices, emerges as a network with a powerlaw degree distribution P(k)~k^{ γ}, where γ=5.66 reveals scalefree coordination number disorder since P(k) also describes the fraction of blocks having k neighbours. To quantify the size disorder, we show that if the ith block is populated with p_{i}~x_{i}^{3}, then its distribution in the WPSL exhibits multifractality.
 Publication:

New Journal of Physics
 Pub Date:
 September 2010
 DOI:
 10.1088/13672630/12/9/093045
 arXiv:
 arXiv:1008.4994
 Bibcode:
 2010NJPh...12i3045H
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Physics  Data Analysis;
 Statistics and Probability;
 Physics  Physics and Society
 EPrint:
 7 pages, 8 figures, To appear in New Journal of Physics (NJP)