the modified substrate. It is unclear at this stage if Haussmann modifications were optimal and more importantly, if they were at a certain point inevitable and would have happened anyway (due to the high level of congestion for example). More work, with more data on a larger spatial scale are probably needed to study these important questions.

Methods {#methods .unnumbered}
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**Temporal Network Data**

We denote by $G_t \equiv G(V_t, E_t)$ the obtained primal graph at time $t$, where $V_t$ and $E_t$ are respectively the set of nodes and links at time $t$. The number of nodes at time $t$ is then $N(t)= |V_t|$ and the number of links is $E(t) = |E_t|$. Using common definitions, we thus have $V_t = V_{t-1} \cup \Delta V_t$ and $E_t =
E_{t-1} \cup \Delta E_t$, where $\Delta V_t$ and $\Delta E_t$ are respectively the new street junctions and the new streets added in time $]t-1,t]$ to the network existing at time $t-1$.

The networks for 1789, 1826, 1836, 1888 are extracted from the following maps:

-   1789: Map of the city of Paris with its new enclosure. Geometrically based on the ‘meridienne de l’Observatoire’ and surveyed by Edmé Verniquet. Achieved in 1791.

-   