Correction to: Scientific Reports https://doi.org/10.1038/s41598-018-22969-4, published online 16 March 2018

This Article contains errors in the following equations:

In the Results section, under the subheading ‘Detecting communities in the African road network’, the equation:

\(\cos \,(\theta )={{\bf{r}}}_{i,j}{{\bf{r}}}_{j,p}/{{\bf{r}}}_{i,j}{{\bf{r}}}_{j,p},\) where \({{\bf{r}}}_{i,j}={{\bf{r}}}_{j}{{\bf{r}}}_{i}\)

should read:

\(\cos \,(\theta )=|{{\bf{r}}}_{i,j}\cdot {{\bf{r}}}_{j,p}|/{{\rm{r}}}_{i,j}{{\rm{r}}}_{j,p},\) where \({{\bf{r}}}_{i,j}={{\bf{r}}}_{j}-{{\bf{r}}}_{i}\)

In addition, under the same subheading, the equation:

\(P(k){k}^{-\gamma }\)

should read:

\(P(k)\sim {k}^{-\gamma }\)

Furthermore, Equation 1:

\({w}_{i,j}=\frac{1}{/{{\boldsymbol{r}}}_{i,j}/}{}_{{{\bf{r}}}_{i}\,}{}^{{{\bf{r}}}_{{{\rm{r}}}_{j}}}m({\bf{r}})p({\bf{r}})d({\bf{r}})\)

should read:

\({w}_{i,j}=\frac{1}{|{{\boldsymbol{r}}}_{i,j}|}{\int }_{{{\bf{r}}}_{i}}^{{{\bf{r}}}_{j}}m({\bf{r}})p({\bf{r}})d{\bf{r}}\)