Motivated by the complexity of network data, we propose a directed hybrid random network that mixes preferential attachment (PA) rules with uniform attachment rules. When a new edge is created, with probability \(p\in (0,1)\), it follows the PA rule. Otherwise, this new edge is added between two uniformly chosen nodes. Such mixture makes the in- and out-degrees of a fixed node grow at a slower rate, compared to the pure PA case, thus leading to lighter distributional tails. For estimation and inference, we develop two numerical methods which are applied to both synthetic and real network data. We see that with extra flexibility given by the parameter p, the hybrid random network provides a better fit to real-world scenarios, where lighter tails from in- and out-degrees are observed.

受网络数据复杂性的启发，我们提出了一种有向混合随机网络，它将优先附件 (PA) 规则与统一附件规则混合在一起。当创建新边时，概率为\(p\in (0,1)\)，它遵循 PA 规则。否则，在两个统一选择的节点之间添加这条新边。与纯 PA 情况相比，这种混合使得固定节点的入出度以较慢的速度增长，从而导致更轻的分布尾部。对于估计和推理，我们开发了两种适用于合成和真实网络数据的数值方法。我们看到，通过参数p给出的额外灵活性，混合随机网络提供了更适合现实世界的场景，在这些场景中，可以观察到来自入度和出度的较轻的尾部。