Comparing spatial networks: A one-size-fits-all efficiency-driven approach.,Physical Review E

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Comparing spatial networks: A one-size-fits-all efficiency-driven approach.
Physical Review E ( IF 2.2 ) Pub Date : 2020-04-01 , DOI: 10.1103/physreve.101.042301
Ignacio Morer _{1,

2} , Alessio Cardillo _{3,

4,

5,

6} , Albert Díaz-Guilera _{1,

2} , Luce Prignano _{1,

2} , Sergi Lozano _{2,

3,

7,

8}

Affiliation

Spatial networks are a powerful framework for studying a large variety of systems belonging to a broad diversity of contexts: from transportation to biology, from epidemiology to communications, and migrations, to cite a few. Spatial networks can be described in terms of their total cost (i.e., the total amount of resources needed for building or traveling their connections). Here, we address the issue of how to gauge and compare the quality of spatial network designs (i.e., efficiency vs. total cost) by proposing a two-step methodology. First, we assess the network's design by introducing a quality function based on the concept of network's efficiency. Second, we propose an algorithm to estimate computationally the upper bound of our quality function for a given network. Complementarily, we provide a universal expression to obtain an approximated upper bound to any spatial network, regardless of its size. Smaller differences between the upper bound and the empirical value correspond to better designs. Finally, we test the applicability of this analytic tool set on spatial network data-sets of different nature.

中文翻译：

比较空间网络：一种适合所有人的，以效率为导向的方法。

空间网络是一个强大的框架，可用于研究各种环境中的各种系统：从交通运输到生物学，从流行病学到通讯，再到移民，等等。可以根据空间网络的总成本（即，建立或移动其连接所需的资源总量）来描述空间网络。在这里，我们通过提出两步法来解决如何衡量和比较空间网络设计质量（即效率与总成本）的问题。首先，我们基于网络效率的概念通过引入质量函数来评估网络的设计。其次，我们提出了一种算法，可以通过计算来估计给定网络的质量函数的上限。相辅相成我们提供一个通用表达式，以获取任何空间网络的近似上限，而不管其大小如何。上限和经验值之间的较小差异对应于更好的设计。最后，我们在不同性质的空间网络数据集上测试了该分析工具集的适用性。

更新日期：2020-04-03

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