Simple models of small world networks with directed links
Disordered Systems and Neural Networks
2009-11-07 v2 Statistical Mechanics
Abstract
We investigate the effect of directed short and long range connections in a simple model of small world network. Our model is such that we can determine many quantities of interest by an exact analytical method. We calculate the function , defined as the number of sites affected up to time when a naive spreading process starts in the network. As opposed to shortcuts, the presence of un-favorable bonds has a negative effect on this quantity. Hence the spreading process may not be able to affect all the network. We define and calculate a quantity named the average size of accessible world in our model. The interplay of shortcuts, and un-favorable bonds on the small world properties is studied.
Cite
@article{arxiv.cond-mat/0205244,
title = {Simple models of small world networks with directed links},
author = {A. Ramezanpour and V. Karimipour},
journal= {arXiv preprint arXiv:cond-mat/0205244},
year = {2009}
}
Comments
15 pages, 9 figures, published version