I think the OP means a consensus path is a join of all the segments where the segments are joined by overlaying identical elements (thus deleting one) at the joining ends. By this rule the two valid "consensus paths" are 

A+ : B+ : E+ : D+ : C-
C+ : D- : E- : B- : A-

[download]

which are the reverse (and sign change) of each other.

I do wish the OP would speak up because I have a sneaking suspicion his real data is not all single letters, and so my solution Re: Formalizing an array type problem, looking for solution above will need "tweaking".

In reply to Re^3: Formalizing an array type problem, looking for solution by Anonymous Monk
in thread Formalizing an array type problem, looking for solution by melmoth

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