the pre-Haussmann period, even if in the period 1789-1826 there was an improvement of centrality concentration, there is an accumulation of central nodes both at short distances ($r<2,500$ meters) and at long distances ($r>2,500$ meters) in the following period (1826-1836). As a result, visually clear in Fig. \[fig:maxvbc\], there is a large concentration of centrality in the center of Paris until 1836 at least. The natural consequence of this concentration is that the center of Paris was very probably very congested at that time. In this respect, what happens under the Haussmann supervision is natural as he acts on the spatial organization of centrality. We see indeed that in 1888, the most central nodes form a more reticulated structure excluding concentration of centrality. A structure which remained stable until now. Interestingly, we note that Haussmann’s new roads and avenues represent approximately $6\%$ of the total length only (compared to nowadays network), which is a small fraction, considered that it has a very important impact on the centrality spatial organization.

This reorganization of centrality was undertaken with creation of new roads and avenues destroying parts of the original pattern (see Fig. \[fig:map\_H\] and Fig. \[fig:maps\](b)) resulting in the modification of the 