the order of magnitude can be trusted here. We can compute the number of nodes $N$ versus the population $P$ and we observe a linear dependence with coefficient $dN/dP=0.0021$ (in previous studies, we also found a linear dependence \[24\], but with a linear coefficient equal to $dN/dP=0.019$). It is thus clear that the number of nodes follows the demographic population and that the large increase observed during the Haussmann period is largely due to the demographic pressure.

Type of new links
-----------------

In figure \[fig:newlinks1\], we show the evolution of the proportion of the different types of new links. We see in this figure that the evolution is rather smooth and that from this point of view, the Haussmann period is not radically different from previous ones.

Stability of the BC distribution
--------------------------------

We consider here the evolution of the vertex BC with time. In figure \[fig:SI\_fig2\], we see that the average BC decreases slightly and that the overall probability distribution remains constant in time.

Most central nodes: stability of spatial patterns
-------------------------------------------------

The most central nodes are such as their centrality is $g_v>\max{g_v}/\alpha$. In the letter we consider $\alpha=10$ and we show in figure \[fig:alpha\] the results for $\alpha=5$ 