The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two independent pure birth processes that are observed at a common exponentially distributed time T (thus creating dependence between in- and out-degree). The characterization gives an explicit form for the joint degree distribution, and this confirms previously derived tail probabilities for the two marginal degree distributions. The new characterization is also used to obtain an explicit expression for tail probabilities in which both degrees are large. A new generalized directed preferential attachment model is then defined and analyzed using similar methods. The two extensions, motivated by empirical evidence, are to allow double-directed (i.e. undirected) edges in the network, and to allow the probability of connecting an ingoing (outgoing) edge to a specified node to also depend on the out-degree (in-degree) of that node.

中文翻译：

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定向优先依恋模型：限制度分布及其尾部

重新审视了定向优先依恋模型。限制入度和出度分布的新精确表征由两个给出独立的在共同的指数分布时间观察到的纯出生过程吨（从而在入度和出度之间产生依赖性）。表征给出了联合度分布的明确形式，这证实了先前导出的两个边缘度分布的尾部概率。新的表征也用于获得两个度都很大的尾部概率的显式表达式。然后使用类似的方法定义和分析一个新的广义定向优先附着模型。由经验证据推动的两个扩展是允许网络中的双向（即无向）边，并允许将传入（传出）边连接到指定节点的概率也取决于出度（该节点的度数）。