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

Authors
Citation
Cf. Moukarzel, Spreading and shortest paths in systems with sparse long-range connections, PHYS REV E, 60(6), 1999, pp. R6263-R6266
Citations number
17
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW E
ISSN journal
1063651X → ACNP
Volume
60
Issue
6
Year of publication
1999
Part
A
Pages
R6263 - R6266
Database
ISI
SICI code
1063-651X(199912)60:6<R6263:SASPIS>2.0.ZU;2-8
Abstract
Spreading according to simple rules (e.g., of fire or diseases) and shortes t-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 ca lculated 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 di stance r. It is found that l(r)similar to r for r<r(c)=[2p Gamma(d)(d-1)!]( -1/d) log(2p Gamma(d)L(d)) and l(r)similar to r(c) for r>r(c). The characte ristic length r(c), which governs the behavior of shortest-path lengths, di verges logarithmically with L for all p>0. [S1063-651X(99)50312-7].