Dynamics on spatial networks and the effect of distance coarse graining
- Zeng, An Department of Systems Science, School of Management and Center for Complexity Research, Beijing Normal University, China - Department of Physics, University of Fribourg, Switzerland
- Zhou, Dong Department of Systems Science, School of Management and Center for Complexity Research, Beijing Normal University, China
- Hu, Yanqing Department of Systems Science, School of Management and Center for Complexity Research, Beijing Normal University, China
- Fan, Ying Department of Systems Science, School of Management and Center for Complexity Research, Beijing Normal University, China
- Di, Zengru Department of Systems Science, School of Management and Center for Complexity Research, Beijing Normal University, China
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23.06.2011
Published in:
- Physica A: Statistical Mechanics and its Applications. - 2011, vol. 390, no. 21-22, p. 3962-3969
English
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
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Physique
- Language
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- English
- Classification
- Physics
- License
- License undefined
- Identifiers
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- RERO DOC 27328
- DOI 10.1016/j.physa.2011.06.012
- Persistent URL
- https://folia.unifr.ch/unifr/documents/302097
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