Department of Veterinary Sciences, University of Turin, 10095 Grugliasco, Turin, Italy.
Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Universidad Carlos III de Madrid, E-28911 Leganés, Madrid, Spain.
Phys Rev E. 2017 Nov;96(5-1):052316. doi: 10.1103/PhysRevE.96.052316. Epub 2017 Nov 30.
The study of complex networks, and in particular of social networks, has mostly concentrated on relational networks, abstracting the distance between nodes. Spatial networks are, however, extremely relevant in our daily lives, and a large body of research exists to show that the distances between nodes greatly influence the cost and probability of establishing and maintaining a link. A random geometric graph (RGG) is the main type of synthetic network model used to mimic the statistical properties and behavior of many social networks. We propose a model, called REDS, that extends energy-constrained RGGs to account for the synergic effect of sharing the cost of a link with our neighbors, as is observed in real relational networks. We apply both the standard Watts-Strogatz rewiring procedure and another method that conserves the degree distribution of the network. The second technique was developed to eliminate unwanted forms of spatial correlation between the degree of nodes that are affected by rewiring, limiting the effect on other properties such as clustering and assortativity. We analyze both the statistical properties of these two network types and their epidemiological behavior when used as a substrate for a standard susceptible-infected-susceptible compartmental model. We consider and discuss the differences in properties and behavior between RGGs and REDS as rewiring increases and as infection parameters are changed. We report considerable differences both between the network types and, in the case of REDS, between the two rewiring schemes. We conclude that REDS represent, with the application of these rewiring mechanisms, extremely useful and interesting tools in the study of social and epidemiological phenomena in synthetic complex networks.
复杂网络的研究，特别是社会网络的研究，主要集中在关系网络上，抽象了节点之间的距离。然而，空间网络在我们的日常生活中极其相关，大量的研究表明节点之间的距离极大地影响了建立和维持连接的成本和概率。随机几何图（RGG）是用于模拟许多社交网络的统计属性和行为的主要合成网络模型类型。我们提出了一种称为 REDS 的模型，它扩展了能量约束的 RGG，以考虑与邻居分担链路成本的协同效应，这在真实的关系网络中是可以观察到的。我们应用了标准的 Watts-Strogatz 重连过程和另一种保持网络度分布的方法。第二种技术是为了消除受重连影响的节点之间的度的空间相关性的不必要形式而开发的，从而限制了对其他属性（如聚类和聚类系数）的影响。我们分析了这两种网络类型的统计属性及其作为标准易感染-感染-易感染隔间模型的基质的流行病学行为。我们考虑并讨论了随着重连的增加和感染参数的变化，RGG 和 REDS 之间的属性和行为的差异。我们报告了 RGG 之间以及 REDS 之间（在 REDS 的情况下）两种重连方案之间的相当大的差异。我们的结论是，REDS 代表了在合成复杂网络中研究社会和流行病学现象的极其有用和有趣的工具，通过应用这些重连机制。
