  Connections between microscopic follow-the-leader and macroscopic
fluid-dynamics traffic flow models are already well understood in the case of
vehicles moving on a single road. Analogous connections in the case of road
networks are instead lacking. This is probably due to the fact that macroscopic
traffic models on networks are in general ill-posed, since the conservation of
the mass is not sufficient alone to characterize a unique solution at
junctions. This ambiguity makes more difficult to find the right limit of the
microscopic model, which, in turn, can be defined in different ways near the
junctions. In this paper we show that a natural extension of the first-order
follow-the-leader model on networks corresponds, as the number of vehicles
tends to infinity, to the LWR-based multi-path model introduced in [Bretti et
al., Discrete Contin. Dyn. Syst. Ser. S, 7 (2014)] and [Briani and Cristiani,
Netw. Heterog. Media, 9 (2014)].
