Sparse random hypergraphs: Non-backtracking spectra and community detection. (arXiv:2203.07346v2 [math.PR] UPDATED)

We consider the community detection problem in a sparse $q$-uniform
hypergraph $G$, assuming that $G$ is generated according to the so-called
Hypergraph Stochastic Block Model (HSBM). We prove that a spectral method based
on the non-backtracking operator for hypergraphs works with high probability
down to the generalized Kesten-Stigum detection threshold conjectured by
Angelini et al. We characterize the spectrum of the non-backtracking operator
for the sparse HSBM, and provide an efficient dimension reduction procedure
using the Ihara-Bass formula for hypergraphs. …

arxiv backtracking community detection math random