2002/09/12 by Damián H. Zanette, Damian H. Zanette
Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1209/epl/i2002-00670-x
6 pages, 2 figures, submitted to Europhys. Lett
arxiv created 2002/09/12 · openalex publication_date 2002/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We report numerical simulations of a strongly biased diffusion process on a one-dimensional substrate with directed shortcuts between randomly chosen sites, i.e. with a small-world–like structure. We find that, unlike many other dynamical phenomena on small-world networks, this process exhibits non-monotonic dependence on the density of shortcuts. Specifically, the diffusion time over a finite length is maximal at an intermediate density. This density scales with the length in a nontrivial manner, approaching zero as the length grows. Longer diffusion times for intermediate shortcut densities can be ascribed to the formation of cyclic paths where the diffusion process becomes occasionally trapped.