# Strong Collapse of Random Simplicial Complexes

arXiv: https://arxiv.org/abs/2301.03514 · HTML: https://mlsanity.com/paper/2301.03514/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2023.

## Built on by (most cited first, 1 of 1)

- [Contraction and Hourglass Persistence for Learning on Graphs, Simplices, and Cells](https://mlsanity.com/paper/2604.17548/) (2026)

## Abstract (arXiv)

The strong collapse of a simplicial complex, proposed by Barmak and Minian (Disc. Comp. Geom. 2012), is a combinatorial collapse of a complex onto its sub-complex. Recently, it has received attention from computational topology researchers, owing to its empirically observed usefulness in simplification and size-reduction of the size of simplicial complexes while preserving the homotopy class. We consider the strong collapse process on random simplicial complexes. For the ErdHos-R'enyi random clique complex X(n,c/n) on n vertices with edge probability c/n with c>1, we show that after any maximal sequence of strong collapses the remaining subcomplex, or core must have (1-γ)(1-cγ) n+o(n) vertices asymptotically almost surely (a.a.s.), where γ is the least non-negative fixed point of the function f(x) = expleft(-c(1-x)right) in the range (0,1). These are the first theoretical results proved for strong collapses on random (or non-random) simplicial complexes.