In Huckel Method, by numbering the sp2 carbons in a molecule with conjugated double bonds, we can assemble its secular determinant in a form similar to the adjacency matrix of a graph. Taking trans-stilbene as a example:
Its secular determinant takes this simplified form:
[[x,1,0,0,0,1,0,0,0,0,0,0,0,0], [1,x,1,0,0,0,0,0,0,0,0,0,0,0], [0,1,x,1,0,0,0,0,0,0,0,0,0,0], [0,0,1,x,1,0,0,0,0,0,0,0,0,0], [0,0,0,1,x,1,0,0,0,0,0,0,0,0], [1,0,0,0,1,x,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,x,1,0,0,0,0,0,0], [0,0,0,0,0,0,1,x,1,0,0,0,0,0], [0,0,0,0,0,0,0,1,x,1,0,0,0,1], [0,0,0,0,0,0,0,0,1,x,1,0,0,0], [0,0,0,0,0,0,0,0,0,1,x,1,0,0], [0,0,0,0,0,0,0,0,0,0,1,x,1,0], [0,0,0,0,0,0,0,0,0,0,0,1,x,1], [0,0,0,0,0,0,0,0,1,0,0,0,1,x]]
To convert it to a adjacency matrix, it's necessary just to replace the x variables in the main diagonal with zeroes.
Now the problem is: if we start with the adjacency matrix, not knowing the structure beforehand, one needs to grab pen and paper and do a bit of scribbling to see the shape it represents, as that information is not apparent just by glancing at the matrix. This procedure is a bit slow and error-prone when the molecule is large.
I noticed WolframAlpha allows us to get a graph representation from the adjacency matrix, as shown here for Benzene, but as the site uses proprietary software, we soon run into artificial limitations. My stilbene matrix exceeds maximum character limit, for example:
And it also can't be automated for larger number of structures.
So I'd like to ask some recommendations on how to do the same, but using Free / Open Source Software. Python libraries would be great, to ease automation.