Hi,
I suppose that your requirement is to remove "dangle" lines recursively from the network, so that the resulting network contains only lines belonging to a cycle or a circuit.
An interesting challenge. I would try that by creating a custom transformer with Loop.
e.g.

A "dangle" line touches a node that touches just one line. You can determine that a node touches how many lines by testing the number of elements of the "_node_angle{}" list created by the TopologyBuilder.
The SpatialFilter outputs "dangle" lines from the Passed port, "non-dangle" lines from the Failed port.
The FeatureMerger merges one "dangle" line to every "non-dangle" line unconditinally.
If a "dangle" line existed, all the "non-dangle" lines will be output from the Merged port of the FeatureMerger and go to the Input port (next iteration) through the Loop port.
Otherwise, they will be output from the NotMerged port --> Output port, and the iteration will finish.
Note that this custom transformer must be always linked because it contains blocking-transformers with Loop.
Takashi