Question: Find all possible subgraph isomorphic to H in a Graph G

Given Graph G and Graph H how to store the list of all the various Subgraphs of Shape H in G with their vertex labels.

I have write a code but it may not be the optimal way to do it and it may be time consuming for even medium graphs too

Any way to optimize

Let From this list of subgraphs H of say [G0,G1,G2,.....] we pick NumberOfVertices(G) Graphs
say H= [H0,H1,H2,H3,....,Hn]

i) Now any two graph Hi,Hj have excatly one edge interection if (i,j) is an edge in G

 ii) An edge in  the list H will occur exactly twice only in the entire list of graphs

If these two conditions satifies all such H I need to save

Toycode until picking graphs

From that how to pick lists which satify conditions i) and ii) is another need help

Toy_code.mw