Dear Researchers,

I proposed a new method, called Optinalysis, for symmetry detection, similarity and identity measure between two automorphic or isomorphic graphs.

I tested the method using the following example datasets in comparisons. The results look amazing and interesting. You can give a comment of feedback regarding the method.

Thank you for your time.

Example Datasets

A1 = (25, 28, 15, 7, 9, 0, 4, 6, 3, 16)

The iso-polymorphs of A1 graph are (in this case, we mind more importantly the position specific variations of the sequence).

B1 = (25+t, 28, 15, 7, 9, 0, 4, 6, 3, 16)

B2 = (25, 28+t, 15, 7, 9, 0, 4, 6, 3, 16)

B9 = (25, 28, 15, 7, 9, 0, 4, 6, 3+t, 16)

B10 = (25, 28, 15, 7, 9, 0, 4, 6, 3, 16+t)

Let t be 10, 25, 50, 100, 103, 104...... 1010

Then, the similarity scores (following the methodology proposed) between the graph A1 and each of set B(1-10) were obtained as Q, for each t.

Let G be a set of positive integers ranking the sequence of skewed positions of graph B(1-10) as B1=1, B2=2, B3=3, B4=4, … B10=10.

By plotting regression graphs of G against Q, I observed a moving and changing regression patterns (from the best fits of linear, polynomial, and exponential models, to continues polynomial models) as t approaches a certain limit.

Therefore, the method shows that the relationship between the datasets A and B is deterministic on polynomial and non-polynomial graph models.

Details of the proposed method is explained in a preprinted manuscript at doi: 10.20944/preprints202008.0072.v1

File attached is an easy way to go about the solution of the problem graphically.