A generalized configuration space on $X$ consists of a collection of points on $X$ with specific rules governing which points cannot coincide. In this work, I will introduce a new algebraic structure, called a "contractad," on the union of these spaces for $X = R^n$, which extends the concept of the little discs operad. I will demonstrate how this algebraic framework can be used to extract information regarding the Hilbert series of cohomology rings. Surprisingly, the same approach can be applied to generate a series of combinatorial data associated with graphs, such as the number of Hamiltonian paths, Hamiltonian cycles, acyclic orientations, and chromatic polynomials. The talk is based on the joint work with D.Lyskov.