Send to

Choose Destination
See comment in PubMed Commons below

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

Author information

Instituto de Física, Universidade Federal Fluminense, CEP 24210-340, Niterói, RJ, Brazil.


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 r<r(c)=[2p Gamma(d)(d-1)!](-1/d) log(2p Gamma(d)L(d)) and l(r) approximately r(c) for r>r(c). The characteristic length r(c), which governs the behavior of shortest-path lengths, diverges logarithmically with L for all p>0.

PubMed Commons home

PubMed Commons

How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for American Physical Society
    Loading ...
    Support Center