from $G_t$ and we denote this graph as $G_t \setminus \{ e^* \}$. We compute again the average edge betweenness centrality, this time for the graph $G_t \setminus \{
e^* \}$. Finally, the impact $\delta(e^*)$ of edge $e^*$ on the betweenness centrality of the network at time $t$ is defined as $$\delta(e^*) = \frac { \left[\overline{g}(G_t) -  \overline{g}( G_t \setminus \{ e^* \} ) \right] }{
 \overline{g}(G_t)}$$ The BC impact is thus the relative variation of the graph average betweenness due to the removal of the link $e^*$.

**Form factor**

The shape or form factor $\phi$ of blocks is defined as the ratio of the area of the block and the area of the circumscribed circle of diameter $D$ (see [@Lammer:2006; @Barthelemy:2011]) $$\phi=\frac{A}{\pi D^2/4}$$ The more anisotropic the block and the smaller the factor $\phi$.

Supplementary Information {#supplementary-information .unnumbered}
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Population and nodes
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In figure \[fig:popu\], we show the evolution of the number of nodes and of the population of Paris (for the 12 districts delimited by the ‘fermiers generaux’ for the period 1789-1851 and after for the 20th districts of Paris).

The area under consideration for the calculation of the population is not exactly the same, and only 