I have a list (of lists) and like to identify elements that have the same "structure"! Here is a minimal example:

example = { {{m1,m2},{m2,m4}} , {{m1,m2},{m1,m4}} }

This list has two elements {{m1,m2},{m2,m4}} and {{m1,m2},{m1,m4}} (which both are lists again). Now, in the problem I am working on each element is associated to a product of Kronecker deltas according to

{{m1,m2},{m2,m4}} -> delta(m1,m2) delta(m2,m4)

with delta(i,j) the Kronecker delta. In that sense, {{m1,m2},{m2,m4}} and {{m1,m2},{m1,m4}} are mathematically identical (have the "same structure").

Question: How can I write a Mathematica code that identifies these elements as the same and returns me a new list, where each element with the same structure appears only once together with its "multiplicity" in the original list?

My (failed) solution: I thought I could work with graphs and associate graphs G1 and G2 to {{m1,m2},{m2,m4}} and {{m1,m2},{m1,m4}}, respectively, with corresponding edges as indicated by the pairs. Then, G1 and G2 literally look the same, yet when I try

`Tally[{G1,G2}]'

I do not get {G1,2}, but {{G1,1},{G2,1}}. So somehow Mathematica is unable to identify graphs with the "same structure" as the same.

How can I solve the problem? Any hint is greatly appreciated! Many thanks!