RivEX can attribute your river network in several ways.  It can calculate and assign values to each polyline of the network.  

Stream ordering is the classic example of river analysis and is an important part of river network analysis.  Many environmental variables are often correlated to stream order. 

To calculate a network attribute such as stream order, you must have a unique ID number for each polyline and populated From- and To- node fields in the attribute table of your river network.  These must be built before attempting to attribute your network. Your river network must conform to the RivEX  input specifications.

Once you have set the layer to process, polyline ID, the node fields and workspace you can click on the BUILD button. Once the build process has completed the Tools panel activates and you can expand the Attribute Network node.  Simply check the Run network attribution tools and click on Run Tool.

Run Attributes Tool

RivEX allows you to compute:

Strahler order

Shreve order

The sum of upstream lengths 

The type of link 

Catchment ID 

Main Channel 

Distance from network mouth 

Identify loops/braided sections

Source ID and encode back into network

Accumulate an attribute in the network

Encode Hack stream order

Warning Tools that extract lengths will be in the units of the dataset. This won't make much sense if the dataset is in decimal degrees and would in fact cause other RivEX tools to process the network incorrectly. If your network is not in units of meters you must project your dataset into a coordinate system that is. See more advice here.