最近邻有向双曲随机图
Nearest-neighbour directed random hyperbolic graphs
AI总结：
提出最近邻有向双曲随机图模型及其规范版本，研究局部键长、入度、互反性等特性，发现网络具有核心-边缘结构和截断幂律分布，并可通过类温度参数调节互反性。
摘要：
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。在此我们提出了一个简单的有向双曲模型，其中在双曲盘上随机分布的节点连接到固定数量m的最近空间邻居。我们还引入了该网络的规范版本（我们称之为“具有可变连接半径的网络”），其中出键的最大长度依赖于空间，并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、入度和互反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-边缘结构。我们证明，对于小密度的节点，整体入度具有截断幂律分布。我们证明，通过调整一个额外的类温度参数，可以在不改变网络其他全局属性的情况下调节网络的互反性。
英文摘要：
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 neighbours. 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 spatial 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.
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