Check for Features to touch boundary

Hello

Im thinking about a problem to solve for a while now, but cant find a good approach...

Here is my problem:

i have a feature class with lots of line features. The line features equal segements and a segment touches only one other segment.

Now i need to sort them.
From a starting segement, i want to look up the one that touches the boundary to the next segment (and write a new attribute to this segment, eq iterating numbers). From this second segement, i want to look for the third one, and so on.

Does anyone has a good hint how to achieve that?
some pseudo code would be deeply appreciates.

greetings tom