标题： 带异常的偏好连接网络中的度分布 显示英文标题

标题： Degrees in Preferential Attachment Networks with an Anomaly

摘要： 我们考虑了一种包含异常的偏好附着模型。我们的目标是通过研究异常对网络结构特性的影响来理解在网络出现异常前后网络的演变。异常的存在使得在它到达后以固定概率吸引新添加的边。我们调查了网络中节点度的增长情况，发现异常的度几乎线性增长。我们还提供了普通节点极限度分布指数的经验推导，并研究了最老节点的度增长情况。我们证明，当异常早期进入时，度分布会显著改变，而晚期异常则影响甚微。我们的分析为理解具有异常节点的偏好附着网络的演变提供了更深刻的见解。 显示英文摘要

摘要： We consider a preferential attachment model that incorporates an anomaly. Our goal is to understand the evolution of the network before and after the occurrence of the anomaly by studying the influence of the anomaly on the structural properties of the network. The anomaly is such that after its arrival it attracts newly added edges with fixed probability. We investigate the growth of degrees in the network, finding that the anomaly's degree increases almost linearly. We also provide a heuristic derivation for the exponent of the limiting degree distributions of ordinary vertices, and study the degree growth of the oldest vertex. We show that when the anomaly enters early, the degree distribution is altered significantly, while a late anomaly has minimal impact. Our analysis provides deeper insights into the evolution of preferential attachment networks with an anomalous vertex.