移动通信网络的地理分散
Geographical dispersal of mobile communication networks
摘要：
在本文中，我们分析了一个通信网络的统计特性，从移动电话公司的记录。该网络由250万客户组成，他们在6个月内进行了8.1亿次通信（电话和短信），我们拥有他们的地理位置信息。它表明，在这个网络的度分布有一个幂律度分布$k^{-5}$和两个客户连接的链接的概率遵循重力模型，即减少像$d^{-2}$，其中$d$是客户之间的距离。我们还考虑了通信三角形的地理扩展，我们表明，通信三角形不仅由地理上相邻的节点，但它们可能会延伸很大的距离。这最后一个属性是没有捕获的地理网络的现有模型，在最后一节中，我们提出了一个新的模型，再现所观察到的属性。我们的模型，这是基于迁移和代理的本地适应，然后分析研究和由此产生的预测证实了计算机模拟。
英文摘要：
In this paper, we analyze statistical properties of a communication network constructed from the records of a mobile phone company. The network consists of 2.5 million customers that have placed 810 millions of communications (phone calls and text messages) over a period of 6 months and for whom we have geographical home localization information. It is shown that the degree distribution in this network has a power-law degree distribution $k^{-5}$ and that the probability that two customers are connected by a link follows a gravity model, i.e. decreases like $d^{-2}$, where $d$ is the distance between the customers. We also consider the geographical extension of communication triangles and we show that communication triangles are not only composed of geographically adjacent nodes but that they may extend over large distances. This last property is not captured by the existing models of geographical networks and in a last section we propose a new model that reproduces the observed property. Our model, which is based on the migration and on the local adaptation of agents, is then studied analytically and the resulting predictions are confirmed by computer simulations.
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