Realistic searches on stretched exponential networks

Abstract

We consider navigation or search schemes on networks which have a degree distribution of the form P(k) ∝ exp(−k γ). In addition, the linking probability is taken to be dependent on social distances and is governed by a parameter λ. The searches are realistic in the sense that not all search chains can be completed. An estimate of µ = ρ/s d, where ρ is the success rate and s d the dynamic path length, shows that for a network of N nodes, µ ∝ N −δ in general. Dynamic small world effect, i.e., δ ≃ 0 is shown to exist in a restricted region of the λ−γ plane.