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RivEX requires your river network to be topologically correct for it to successfully process. Various errors can occur when a network is created and/or updated.

RivEX provides a set of quality controls which you can run on your network.  The output of a quality control is a table in a File GeoDatabase identifying the polylines which failed the quality control.  It is then up to you, the user, to correct your data.
More advice is given in the manual about dealing with these errors:

Polyline attributes

Null (zero) length polylines

Multi-part polylines

Self-intersecting polylines

Closed (looped) polylines

Small polylines composed of two vertices

Disconnected polylines

Double digitised polylines

Intersecting polylines

Overlapping polylines

Duplicate geometry

Sources within network

Network cycles

Polyline spikes

Stacked vertices

RivEX also provides a tool for automatically removing self-intersections

Quality controlling your river network