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arXiv · 2603.01268

Achievability of Heterogeneous Hypergraph Recovery from its Graph Projection

Alexander Morgan·Chenghao Guo
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Abstract

We formulate and analyze a heterogeneous random hypergraph model, and we provide an achieveability result for recovery of hyperedges from the observed projected graph. We observe a projected graph which combines random hyperedges across all degrees, where a projected edge appears if and only if both vertices appear in at least one hyperedge. Our goal is to reconstruct the original set of hyperedges of degree $d_j$ for some $j$. Our achievability result is based on the idea of selecting maximal cliques of size $d_j$ in the projected graph, and we show that this algorithm succeeds under a natural condition on the densities. This achievability condition generalizes a known threshold for $d$-uniform hypergraphs with noiseless and noisy projections. We conjecture the threshold to be optimal for recovering hyperedges with the largest degree.

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Alexander Morgan, Chenghao Guo. 2026-03-01. Achievability of Heterogeneous Hypergraph Recovery from its Graph Projection. https://arxiv.org/abs/2603.01268

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