this period also, densification was the main process in this area).

We then plot the distribution of this quantity $\delta$ for the different transition periods and the result is shown in Fig. \[fig:bcimpact\].

These figures show that for all periods most new links belong to the densification process with a small peak of exploration in the period 1836-1888. In well-developed, mature systems, it is expected that densification is the dominant growth mechanism. Here also, we see that the Haussmann period is not significantly different from previous periods.

**Evolution of the spatial distribution of centrality**

The betweenness centrality (BC) $g_v(i)$ of a node $i$ is defined in the Methods section and essentially measures the fraction of times a given node is used in the shortest paths connecting any pair of nodes in the network, and is thus a measure of the contribution of a link in the organisation of flows in the network [@Freeman:1977]. In our case where we consider a limited portion of a spatial network, two important effects need to be taken into consideration. First, as we consider a portion, only paths within this portion are taken into account in the calculation of the BC and this usually does 