Subcritical percolation and network archaeology on random recursive tree substrate networks

What the math gives to ML

The paper gives a constructive way to recover tree-like structure from a cyclic graph: independently thin edges, contract retained tree components into weighted blobs, and analyze the shortcut layer as a rank-one random graph. The transferable asset is the explicit subcriticality control \(\rho=p\lambda/(1-2p)<1\), which prevents a percolated graph from collapsing into one giant shortcut-connected component, together with Jordan centrality computed after vertex deletion. In graph neural networks, this can become a stochastic graph-view generator and a topology-aware node-ranking/readout module, especially for source localization, graph-level pooling, and robustness training.