A novel approach for studying realistic navigations on networks

Abstract

We consider navigation or search schemes on networks which are realistic in thesense that not all search chains can be completed. We show that the quantityμ = ρ/sd,where sd is the average dynamic shortest distance andρ the success rate for completion of a search, is a consistent measure for the quality of asearch strategy. Taking the example of realistic searches on scale free networks, we find thatμ scales withthe system size N as N−δ,where δ decreases as the searching strategy is improved. This measure is also shownto be sensitive to the distinguishing characteristics of networks. In thisnew approach, a dynamic small world (DSW) effect is said to exist whenδ≈0. We show that such a DSW does indeed exist in social networks in which the linkingprobability is dependent on social distances.