Kasyanov I A, van der Hoorn P, Krioukov D, Tamm M V
Independent researcher, 0105 Tbilisi, Georgia.
Eindhoven University of Technology, 5612 AZ Eindhoven, Netherlands.
Phys Rev E. 2023 Nov;108(5-1):054310. doi: 10.1103/PhysRevE.108.054310.
Undirected hyperbolic graph models have been extensively used as models of scale-free small-world networks with high clustering coefficient. Here we presented a simple directed hyperbolic model where nodes randomly distributed on a hyperbolic disk are connected to a fixed number m of their nearest spatial neighbors. We introduce also a canonical version of this network (which we call "network with varied connection radius"), where maximal length of outgoing bond is space dependent and is determined by fixing the average out-degree to m. We study local bond length, in-degree, and reciprocity in these networks as a function of spacial coordinates of the nodes and show that the network has a distinct core-periphery structure. We show that for small densities of nodes the overall in-degree has a truncated power-law distribution. We demonstrate that reciprocity of the network can be regulated by adjusting an additional temperature-like parameter without changing other global properties of the network.
无向双曲图模型已被广泛用作具有高聚类系数的无标度小世界网络模型。在此，我们提出了一种简单的有向双曲模型，其中随机分布在双曲圆盘上的节点与固定数量(m)的最近空间邻居相连。我们还引入了该网络的一个规范版本（我们称之为“连接半径可变的网络”），其中出边的最大长度取决于空间，并且通过将平均出度固定为(m)来确定。我们研究了这些网络中局部键长、入度和互惠性作为节点空间坐标的函数，并表明该网络具有明显的核心-外围结构。我们表明，对于低密度节点，总体入度具有截断幂律分布。我们证明，通过调整一个类似温度的附加参数，可以在不改变网络其他全局属性的情况下调节网络的互惠性。
