Figure 2

Reduction of simplicial complex size. The figure shows an example of simplicial complex (a) and its correspondent dual complex (b). Each facet of the original simplicial complex is represented by a node in the dual complex, and \(k+1\) nodes span a k-simplex if the corresponding \(k+1\) facets have at least a node in common. In both simplicial complexes, the facets are colored according to their dimension. It is easy to see that applying the complexity reduction to the simplicial complex (a) reduces the total number of simplices from 91 to 28, while fixing the homology (both complexes have one connected component, and one hole (1-dimensional cycle).