AI 中文总结
研究随机递归树基底网络的网络考古学问题，利用辅助亚临界键渗流揭示树状重整化结构，通过在最大辅助渗流组件内应用乔丹中心性，为循环网络构建确定性大小的根置信集。
AI 中文摘要
我们研究了一个动态图的网络考古学问题，其潜在基底是随机递归树，观察到的拓扑结构通过独立的齐次埃尔德什-雷尼捷径层得到丰富。目标是从单个未标记的快照为第一个顶点构建一个确定性大小的置信集。由于捷径边会产生循环，通常基于树使用乔丹中心性的论证不能直接应用。我们的方法使用辅助亚临界键渗流来揭示一种树状重整化结构：保留的递归树簇形成重尾团块，保留的捷径通过亚临界一阶随机图连接这些团块，大的组件是由亚临界捷径片段装饰的主导主干团块。然后在最大的辅助渗流组件内应用乔丹中心性，为循环观察到的网络给出一个确定性大小的根置信集。
英文摘要
We study a network-archaeology problem for a dynamic graph whose latent substrate is a random recursive tree and whose observed topology is enriched by an independent homogeneous Erdős-Rényi shortcut layer. From a single unlabeled snapshot, the goal is to construct a confidence set of deterministic size for the first vertex. Since shortcut edges create cycles, the usual tree-based arguments using Jordan centrality do not apply directly. Our method uses auxiliary subcritical bond percolation to expose a tree-like renormalized structure: retained recursive-tree clusters form heavy-tailed blobs, retained shortcuts connect these blobs through a subcritical rank-one random graph, and large components are leading backbone blobs decorated by subcritical shortcut pieces. Applying Jordan centrality inside the largest auxiliary percolation components then gives a deterministic-size root confidence set for the cyclic observed network.
Comments43 pages, 9 figures
