Dynamics on Spatial Networks and the Effect of Distance Coarse Graining

TL;DR

This paper investigates how distance coarse graining affects the properties and dynamics of spatial networks with power-law distance distributions, revealing that coarse graining shifts optimal exponents but becomes negligible in large networks.

Contribution

It introduces a distance coarse graining method for spatial networks and analyzes its impact on network properties and dynamics, highlighting effects on optimal exponents and network functions.

Findings

Distance coarse graining shifts optimal exponents in spatial networks.

In large networks, the effect of coarse graining becomes negligible.

Coarse graining can enhance specific functions of spatial networks.

Abstract

Very recently, a kind of spatial network constructed with power-law distance distribution and total energy constriction is proposed. Moreover, it has been pointed out that such spatial networks have the optimal exponents $\delta$ in the power-law distance distribution for the average shortest path, traffic dynamics and navigation. Because the distance is estimated approximately in real world, we present an distance coarse graining procedure to generate the binary spatial networks in this paper. We find that the distance coarse graining procedure will result in the shifting of the optimal exponents $\delta$. Interestingly, when the network is large enough, the effect of distance coarse graining can be ignored eventually. Additionally, we also study some main dynamic processes including traffic dynamics, navigation, synchronization and percolation on this spatial networks with coarse grained distance. The results lead us to the enhancement of spatial networks' specifical functions.