Flow direction in the network

[MohamadAchour]

Hello,

I have this vector network and I need to drain it to the outlet blue point. In fact,

I need the raster flow direction of the network.

I don’t have the true direction of the segments (from node to node are arbitrary)

And I don’t have a DEM.

Is there any way to do it?

NB: This file was an image in a book, and I converted it to a vector shapefile in ArcMap