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Figure 3 | EPJ Data Science

Figure 3

From: The shape of collaborations

Figure 3

Performance of reduction of simplicial complex size. The panels show the total simplex number (solid lines) and the upper bound (dashed lines) for simplicial complexes built with facet size sequence sampled from the exponential (left), Zipf distribution (middle) and Poisson (right). On the x-axis we plot (from left to right) the power law exponent γ, the average value λ and the exponent ν. It is easy to see that in all cases and for a range of parameters there is a large reduction in simplex number going from K to \(\chi(K)\). Moreover, the bounds on \(n(K)\) and \(n(\chi(K))\), although not tight, reflects closely that between \(n(K)\) and \(n(\chi (K))\) and can therefore be used as a good proxy to decide whether applying the simplicial reduction χ is appropriate or not.

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