Wu Zhihao, Menichetti Giulia, Rahmede Christoph, Bianconi Ginestra
Beijing Key Lab of Traffic Data Analysis and Mining, School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China.
Department of Physics and Astronomy and INFN Sez. Bologna, Bologna University, Viale B. Pichat 6/2 40127 Bologna, Italy.
Sci Rep. 2015 May 18;5:10073. doi: 10.1038/srep10073.
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems.
网络是一种数学结构，被广泛用于描述各种复杂系统，如大脑或互联网。刻画这些网络的几何特性对于路由问题、推理和数据挖掘变得越来越重要。在实际的增长网络中，拓扑、结构和几何特性从其动力学规则中自发出现。然而，我们仍然缺少一个网络发展出涌现复杂几何结构的模型。在这里，我们表明一个单一的双参数网络模型，即增长几何网络，可以生成具有非平凡曲率分布的复杂网络几何结构，将指数增长和小世界特性与有限的谱维数相结合。在一种极限情况下，这些网络的非平衡动力学规则可以生成具有聚类和群落的无标度网络，在另一种极限情况下，可以生成具有非平凡模块化的平面随机几何结构。最后，我们发现几何增长网络的这些特性存在于大量描述生物、社会和技术系统的真实网络中。
