Please guide me about the command to find hosoya index because there's no direct option on Mathematica to find hosoya index. Please tell me that what's the command to find hosoya index on Mathematica?

If there's any other software by which I could find hosoya index please guide me about that

I've developed a program that addresses this problem using Python through transforming the condition of non-incidence to a numerical problem. For example, if we're given an edge set of the graph: $E(G) = \{(1, 2), (2,3), (3,4), (4,5), (5,1)\}$. I simply defined a condition that it checks for the edges with no common vertex and through BSA from the independent edge-set of size one, so on and so forth.

For example: {(2,3)} is an independent singleton. The program then checks for any other edge in the edge set that contains neither 2 or 3 e.g. (4,5). Now it checks for another larger independent edge set. That is whether there is an edge that does not contain (2,3,4,5). The program will do this for every edge singleton. Some results involving the Hosoya index coincide with the results of my program.