Emmerich Thorsten, Bunde Armin, Havlin Shlomo
Institut für Theoretische Physik, Justus-Liebig-Universität Giessen, 35392 Giessen, Germany.
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062806. doi: 10.1103/PhysRevE.89.062806. Epub 2014 Jun 10.
Scale-free networks have been studied mostly as non-spatially embedded systems. However, in many realistic cases, they are spatially embedded and these constraints should be considered. Here, we study the structural and functional properties of a model of scale-free (SF) spatially embedded networks. In our model, both the degree and the length of links follow power law distributions as found in many real networks. We show that not all SF networks can be embedded in space and that the largest degree of a node in the network is usually smaller than in nonembedded SF networks. Moreover, the spatial constraints (each node has only few neighboring nodes) introduce degree-degree anticorrelations (disassortativity) since two high degree nodes cannot stay close in space. We also find significant effects of space embedding on the hopping distances (chemical distance) and the vulnerability of the networks.
无标度网络大多被作为非空间嵌入系统进行研究。然而，在许多实际情况中，它们是空间嵌入的，这些限制因素应该被考虑在内。在此，我们研究一个无标度（SF）空间嵌入网络模型的结构和功能特性。在我们的模型中，链接的度和长度都遵循幂律分布，正如在许多真实网络中所发现的那样。我们表明，并非所有的无标度网络都能嵌入到空间中，并且网络中节点的最大度通常比非嵌入的无标度网络要小。此外，空间限制（每个节点只有很少的相邻节点）会引入度-度反相关性（非相似性），因为两个高度节点在空间中不能靠得很近。我们还发现空间嵌入对跳跃距离（化学距离）和网络脆弱性有显著影响。
