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

  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},
  volume={60 6 Pt A},
  • C. Moukarzel
  • Published 21 May 1999
  • Mathematics, Medicine, Physics
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
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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