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The macroscopic fundamental diagram (MFD) is a large scale description of thetraffic in a urban area and relates the average car flow to the average cardensity. This MFD has been observed empirically in several cities but how itsproperties are related to the structure of the road network has remainedunclear so far. The MFD displays in general a maximum flow $q^*$ for an optimalcar density $k^*$ which are crucial quantities for practical applications.Here, using numerical modeling and dimensional arguments, we propose scalinglaws for these quantities $q^*$ and $k^*$ in terms of the road density, theintersection density, the average car size and the maximum velocity. Thisframework is able to explain the scaling observed empirically for severalcities in the world, such as the scaling of $k^*$ with the road density, therelation between $q^*$ and $k^*$ and the impact of buses on the overallcapacity $q^*$. This work opens the way to a better understanding of thetraffic on a road network at a large urban scale.

Structure of road networks and the shape of the macroscopic fundamental diagram