Topology of random geometric complexes: a survey
نویسندگان
چکیده
منابع مشابه
Random Geometric Complexes
We study the expected topological properties of Čech and Vietoris-Rips complexes built on randomly sampled points in R. These are, in some cases, analogues of known results for connectivity and component counts for random geometric graphs. However, an important difference in this setting is that homology is not monotone in the underlying parameter. In the sparse range, we compute the expectatio...
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In a seminal paper, Erdős and Rényi identified a sharp threshold for connectivity of the random graph G(n, p). In particular, they showed that if p log n/n then G(n, p) is almost always connected, and if p log n/n then G(n, p) is almost always disconnected, as n→∞. The clique complex X (H) of a graph H is the simplicial complex with all complete subgraphs of H as its faces. In contrast to the z...
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ژورنال
عنوان ژورنال: Journal of Applied and Computational Topology
سال: 2018
ISSN: 2367-1726,2367-1734
DOI: 10.1007/s41468-017-0010-0