Hub Neighbor-Degree Diagnostics for Sparse Random Graphs

What the math gives to ML

The paper identifies a structural statistic that distinguishes graphs with nearly identical degree distributions: the mean degree of neighbors conditioned on the degree of the root vertex. Its transferable asset is a degree-conditioned residual profile, especially the contrast between degree-invariant centering in rank-one random graphs and logarithmic growth under preferential attachment. For graph neural networks, this can become a cheap structural-calibration loss or preprocessing diagnostic that detects and controls hub-neighborhood bias without changing the marginal degree sequence. The strongest initial use is to regularize learned edge attention or graph rewiring against unwanted hub assortativity or disassortativity.