# Spreading and shortest paths in systems with sparse long-range connections.

@article{Moukarzel1999SpreadingAS, title={Spreading and shortest paths in systems with sparse long-range connections.}, author={Cristian F. Moukarzel}, journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics}, year={1999}, volume={60 6 Pt A}, pages={ R6263-6 } }

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 V(t) 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 l(r) can be calculated as a function of Euclidean distance r. It is found that l(r) approximately r for…

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