Correction to: Scientific Reports https://doi.org/10.1038/s41598-019-45576-3, published online 25 June 2019
The original version of this Article contained an error in the legend of Figure 1.
“Schematic representation of the alternative small-world model as introduced in19 and discussed in this paper. Much like in the original model, we start with \(N\) nodes placed equidistantly on a ring. However, instead of rewiring, each pair of nodes is connected with distance-based probability \({p}_{d}\) where \(d\) is their minimal distance on the ring. Within distance \(d\le k/2\), nodes are connected with short-range probability \({p}_{S}\). For larger distances, nodes are connected with long-range probability \({p}_{L}={\beta p}_{S}\). With increasing redistribution parameter \(0\le \beta \le 1\) connection probability is redistributed from the short-range regime to the long-range regime while the mean degree \(k\) i“Acknowledgements” on page 9 s kept constant. Hence at \(\beta =0\) the short-range probability is unity while the long-range probability is zero which produces a \(k\)-nearest neighbor lattice. With increasing \(\beta \), long-range “short-cuts” become more probable until at \(\beta =1\) both connection probabilities are equal and thus the model becomes equal to the Erdős–Rényi model.”
now reads:
“Schematic representation of the alternative small-world model as introduced in19 and discussed in this paper. Much like in the original model, we start with \(N\) nodes placed equidistantly on a ring. However, instead of rewiring, each pair of nodes is connected with distance-based probability \({p}_{d}\) where \(d\) is their minimal distance on the ring. Within distance \(d\le k/2\), nodes are connected with short-range probability \({p}_{S}\). For larger distances, nodes are connected with long-range probability \({p}_{L}={\beta p}_{S}\). With increasing redistribution parameter \(0\le \beta \le 1\) connection probability is redistributed from the short-range regime to the long-range regime while the mean degree \(k\) is kept constant. Hence at \(\beta =0\) the short-range probability is unity while the long-range probability is zero which produces a \(k\)-nearest neighbor lattice. With increasing \(\beta \), long-range “short-cuts” become more probable until at \(\beta =1\) both connection probabilities are equal and thus the model becomes equal to the Erdős–Rényi model.”
This error has now been corrected in the PDF and HTML versions of the Article.
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Maier, B.F. Publisher Correction: Generalization of the small-world effect on a model approaching the Erdős–Rényi random graph. Sci Rep 10, 3443 (2020). https://doi.org/10.1038/s41598-020-60474-9
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DOI: https://doi.org/10.1038/s41598-020-60474-9
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