  We introduce a unified framework to compute the solution space properties of
a broad class of combinatorial optimization problems. These properties include
finding one of the optimum solutions, counting the number of solutions of a
given size, and enumeration and sampling of solutions of a given size. Using
the independent set problem as an example, we show how all these solution space
properties can be computed in the unified approach of generic tensor networks.
We demonstrate the versatility of this computational tool by applying it to
several examples, including computing the entropy constant for hardcore lattice
gases, studying the overlap gap properties, and analyzing the performance of
quantum and classical algorithms for finding maximum independent sets.
