Abstract
Spreading according to simple rules (e.g., of fire or diseases) and shortest-path distances are studied on d-dimensional systems with a small density p per site of long-range connections (“small-world” lattices). The volume covered by the spreading quantity on an infinite system is exactly calculated in all dimensions as a function of time t. From this, the average shortest-path distance can be calculated as a function of Euclidean distance r. It is found that for and for The characteristic length which governs the behavior of shortest-path lengths, diverges logarithmically with L for all
- Received 6 August 1999
DOI:https://doi.org/10.1103/PhysRevE.60.R6263
©1999 American Physical Society