Right click the layer and go to symbology and then go to edit symbol. At the top, under properties, from the type dropbox, select cartographic line symbol.
select the line in layers window on the left and on the right select "Arrow at end" what ever suits you.
Oki. Then you must use the azimuth object.
Add new variable (angle_from_y) of cost type to your network dataset, and in evaluators select script evaluation. and write value = edge.fromazimuth in the from-to case and =edge.toazimuth in the to-from evaluator.
build you network and then when you identify the line, you will see the azimuth values. from these azimuth values, you can tell the direction of the digitization.