Can I export a network to Shapefiles or other GIS formats?

No, not directly.
- Export the Vissim model (when holding nodes suitable for a dynamic assignment) to PTV Visum (menu File -> Export -> PTV Visum (Nodes/Edges)…) and then export shapefiles easily from there (menu File -> Export –> Shapefile…).
Note: Take care that the network meets a valid coordinate system.
- Export to 3ds Max