We can then compute the length $\ell$ of a path $P$ $$\ell(P)=\sum_{e\in P}d_e$$ The shortest weighted path is then the one with the minimum total length. The average shortest weighted path is also called the average route distance $d_R$. It indicates on average how many kilometers you have to walk from one point to the other in this spatial network. For a two dimensional network, it is expected [@Barthelemy:2011] that it scales as $$d_R\sim N^{1/2}$$ for a network of size $N$. In order to compare networks with different numbers of nodes $N$, it is then natural to compare the rescaled average route distance $d_R/\sqrt{N}$.

**Betweenness centrality, Impact**

The nature of the growth process can be quantitatively characterised by looking at the centrality of streets. Among the various centrality indices available for spatial networks we use here the betweenness centrality (BC) [@Freeman:1977; @Crucitti:2006; @Porta:2006], which is one of the measures of centrality commonly adopted to quantify the importance of a node or a link in a graph. Given the graph $G_t\equiv
G(V_t,E_t)$ at time $t$, the BC of a link $e$ is defined as: $$g(e) = \sum_{i\in V} \sum_{\stackrel{j \in V} {j \neq i}} 
\frac{\sigma_{ij}(e)}{\sigma_{ij}}$$ where $\sigma_{ij}$ is the number of 