I will try to explain this in a more systematic way: Routes belong to either of two categories: (A) Those whose members can be sorted into a single ordered sequence (B) Those that cannot be sorted into a single ordered sequence of members Sorting makes only sense for category (A) Routes of type (B) can be subdivided into routes of type (A), each of which can be sorted, but the overall route can not be sorted.
Routes are of type (A) if (1) the path from begin to end is identical to the reverse path with all members traversed in the reverse order and in the opposite direction or (2) all members have the role forward or (3) all members have the role backward Any route (1) that has more than two ends or (2) that contains any loop (except the case that the entire route is a single loop) or (3) that contains any element with role forword or role backward (except the cases of all-forward or all-backward) or (4) that contains node or area elements is of type B I am not sure if I have taken care of all cases - please complete as necessary
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