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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Published in:
 Physica A: Statistical Mechanics and its Applications.  2011, vol. 390, no. 2122, p. 39623969
English
Recently, spatial networks have attracted much attention. The spatial network is constructed from a regular lattice by adding longrange 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 longrange 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 tradeoff between the probability density function of longrange 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

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Physics

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https://folia.unifr.ch/unifr/documents/302097
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