Partially Observed Sparse Graphs: The Unknown Sampling Rate is a Tail Index
A large graph is often available only in part: a crawl stopped by its budget, a panel, a partial dump. When the sampled fraction $s$ is known by design the total edge count follows from $\hat e=e_s/s^2$ and no model is needed. We treat the case where $s$ is unknown and the population size is known. Our main result is a reduction: under a sparse exchangeable (graphex) model the expected non-isolated fraction obeys $n_s/n_1\to s^{1+σ}$, so the sampling rate becomes estimable once the tail index $σ$ is, and substituting it back gives $e_s(n_1/n_s)^{2/(1+σ)}$ -- the same estimator, with the design quantity inferred. Estimating global edge cardinality in a sparse graph is therefore, in expecta...
| Authors | Jian Xu, Delu Zeng, John Paisley et al. |
|---|---|
| Primary category | cs.LG |
| Published | 14 August 2026 |
| Last updated at source | 14 August 2026 |
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