A novel approach to study realistic navigations on networks

Details A novel approach to study realistic navigations on networks A novel approach to study realistic navigations on networks

2007-02-23

arxiv.org/abs/physics/0702202v2

Physics

Physics and Society

Text revised, references added; accepted version in Journal of Statistical Mechanics

Scientific paper

10.1088/1742-5468/2007/04/P04007

We consider navigation or search schemes on networks which are realistic in the sense that not all search chains can be completed. We show that the quantity $\mu = \rho/s_d$, where $s_d$ is the average dynamic shortest distance and $\rho$ the success rate of completion of a search, is a consistent measure for the quality of a search strategy. Taking the example of realistic searches on scale-free networks, we find that $\mu$ scales with the system size $N$ as $N^{-\delta}$, where $\delta $ decreases as the searching strategy is improved. This measure is also shown to be sensitive to the distintinguishing characteristics of networks. In this new approach, a dynamic small world (DSW) effect is said to exist when $\delta \approx 0$. We show that such a DSW indeed exists in social networks in which the linking probability is dependent on social distances.

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