I am looking to realize a graph (i.e. write down its adjacency or incidence matrix) given a fundamental cut-set matrix or loop matrix (with respect to an arbitrary spanning tree). Is there some algorithm which can accomplish this task?
I know that given this information, uniqueness cannot be guaranteed due to 2-isomorphism. However, all I want is one compatible graph with the given f-cutset matrix.
There appeared to be some activity on this till the late 1980s, but this problem seems to be dead after this. If anyone has some pointers, it would be of great help. Thanks!
PS: If the f-cutset "matrix" part sounds confusing, or is not part of the conventional vocabulary, just assume that I have listed out all the f-cutsets corresponding to some spanning tree of the graph. Further, self-loops are known to be absent.