Department of Electrical Engineering, Computer Engineering and Informatics, Cyprus University of Technology, 3036 Limassol, Cyprus.
Phys Rev E. 2019 Nov;100(5-1):052313. doi: 10.1103/PhysRevE.100.052313.
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena and the performance of routing algorithms. Yet the mechanisms responsible for their observed characteristics remain elusive. Here we show that many of the observed properties of proximity networks emerge naturally and simultaneously in a simple latent space network model, called dynamic-S^{1}. The dynamic-S^{1} does not model node mobility directly but captures the connectivity in each snapshot-each snapshot in the model is a realization of the S^{1} model of traditional complex networks, which is isomorphic to hyperbolic geometric graphs. By forgoing the motion component the model facilitates mathematical analysis, allowing us to prove the contact, intercontact, and weight distributions. We show that these distributions are power laws in the thermodynamic limit with exponents lying within the ranges observed in real systems. Interestingly, we find that network temperature plays a central role in network dynamics, dictating the exponents of these distributions, the time-aggregated agent degrees, and the formation of unique and recurrent components. Further, we show that paradigmatic epidemic and rumor-spreading processes perform similarly in real and modeled networks. The dynamic-S^{1} or extensions of it may apply to other types of time-varying networks and constitute the basis of maximum likelihood estimation methods that infer the node coordinates and their evolution in the latent spaces of real systems.
临近网络是时变图，用于表示在物理空间中移动的人类之间的接近程度。在过去的十年中，它们的性质得到了广泛的研究，因为它们对传播现象的行为和路由算法的性能有重大影响。然而，负责这些观察到的特性的机制仍然难以捉摸。在这里，我们表明，在一个名为动态 S^{1}的简单潜在空间网络模型中，临近网络的许多观察到的特性自然且同时出现。动态 S^{1}并没有直接对节点移动性进行建模，而是在每个快照中捕获连接性——模型中的每个快照都是传统复杂网络的 S^{1}模型的实现，该模型与双曲几何图形同构。通过放弃运动组件，该模型促进了数学分析，使我们能够证明接触、互接触和权重分布。我们表明，这些分布在热力学极限内是幂律分布，其指数落在真实系统中观察到的范围内。有趣的是，我们发现网络温度在网络动力学中起着核心作用，决定了这些分布的指数、时间聚合的代理度数以及独特和反复出现的组件的形成。此外，我们表明，典型的流行病和谣言传播过程在真实网络和模拟网络中表现相似。动态 S^{1}或其扩展可能适用于其他类型的时变网络，并构成推断真实系统潜在空间中节点坐标及其演化的最大似然估计方法的基础。
