Dynamics on spatial networks and the effect of distance coarse graining

An Zeng, Dong Zhou, Yanqing Hu, Ying Fan and Zengru Di

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 21, 3962-3969

Abstract: Recently, spatial networks have attracted much attention. The spatial network is constructed from a regular lattice by adding long-range edges (shortcuts) with probability P(r)∼r−δ, where r is the geographical distance between the two ends of the edge. Also, a cost constraint on the total length of the additional edges is introduced (∑r=C). It has been pointed out that such networks have optimal exponents δ for the average shortest path, traffic dynamics and navigation. However, when δ is large, too many generated long-range edges will be added to the network. In this scenario, the total cost constraint cannot be satisfied. In this paper, we propose a distance coarse graining procedure to solve this problem. We find that the optimal exponents δ for the traffic process, navigation and synchronization indeed result from the trade-off between the probability density function of long-range edges and the total cost constraint, but the optimal exponent δ for percolation is actually due to dissatisfying the total cost constraint. On the other hand, because the distance coarse graining procedure widely exists in the real world, our work is also meaningful in this aspect.

Keywords: Distance coarse graining; Spatial network; Dynamics (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437111004596
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:21:p:3962-3969

DOI: 10.1016/j.physa.2011.06.012

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().