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.”

“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.”