Simple models of small world networks with directed links

Details Simple models of small world networks with directed links Simple models of small world networks with directed links

2002-05-12

arxiv.org/abs/cond-mat/0205244v2

Phys. Rev. E 66, 036128 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

15 pages, 9 figures, published version

Scientific paper

10.1103/PhysRevE.66.036128

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 $V(T)$, defined as the number of sites affected up to time $T$ 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.

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