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You could then use your downstream trace to select polylines, as RivEX gives each loop family a unique ID you could simply summarize that and then re-select based upon your list of ID's. …

What you are asking to do, tracing along an existing geometry is not a capability of a graphic, which are nothing more than "dumb shapes" drawn onto a map or a layout. Tracing along an existing edge i …

The Trace upstream should then behave. For the record I had to set the weight field (which was length) to be against the digitized direction to make the trace follow the shortest route to source. … I am unsure how this would influence a trace in a more complex scenario such as a river network? …

The enabled field is a flag field which enables or disables an edge within the network. A disabled edge would be as if there was nothing there. This is all discussed in the help file here... As you n …

Select all your segments, maybe you might use a network trace to do that, or you could do it manually. …

From the look of your screen shot it looks like you have used the utility network analyst toolbar and the Trace Upstream option? So... not ArcHydro? …

Set the length to say 50 then I trace up to the length of 50 metres. If my data was a road network in open street map then the data will likely be in WGS84. … So if I had left the length option set to 50 then attempted to Trace along OSM data then I would be allowing a very long trace length. You get a hint here. …

RivEX can link sites, assuming the network is not huge. But I doubt any tool will tell you if the relative direction is u/s or d/s. How do you measure if something is d/s of you, you could initially …

This could be done in model builder using the Trace tool. I can tell you now that that will be painfully slow if you are processing over 100K flags. … Even once you have done the trace you'll need to clip it back as this returns selected edges. As soon as you start fiddling around with geometries you are better off doing that in python. …