我们提出一种有向空间网络模型。该模型以基于年龄的优先连接模型为基础,其中所有弧均从年轻顶点指向年老顶点,并引入概率依赖于两端顶点年龄差的\emph{互逆}连接。该模型生成具有互逆相关性的有向图,具备幂律入度分布和可调的出度分布。我们研究了该模型的两种版本:一种嵌入在$\mathbb{R}^d$中的无限版本,可构造为具有非对称核的权重依赖随机连接模型;另一种是在单位环面上随时间增长的图序列,其局部收敛于无限模型。除了建立两个模型之间的局部极限关系外,我们还研究了度分布、多种有向聚类度量以及有向渗流现象。
We introduce a model for directed spatial networks. Starting from an age-based preferential attachment model in which all arcs point from younger to older vertices, we add \emph{reciprocal} connections whose probabilities depend on the age difference between their end-vertices. This yields a directed graph with reciprocal correlations, a power-law indegree distribution, and a tunable outdegree distribution. We consider two versions of the model: an infinite version embedded in $\mathbb{R}^d$, which can be constructed as a weight-dependent random connection model with a non-symmetric kernel, and a growing sequence of graphs on the unit torus that converges locally to the infinite model. Besides establishing the local limit result linking the two models, we investigate degree distributions, various directed clustering metrics, and directed percolation.