  The number of Bruhat intervals in Coxeter groups is finite, and for the first
few lengths, the intervals were described up to an isomorphism by A. Hultman
using the correspondence between Bruhat intervals and cell decompositions of a
2d sphere and straightforward computations. The main purpose of this paper
consists of a description of the intervals in higher dimensions, as the
Hultman's geometric method is hard to apply due to rapidly growing with length
number of nonisomorphic intervals. We construct an invariant on subintervals in
the Bruhat graphs, using their specific properties. This gives us a method of
comparing two Bruhat interval, that is faster than the general algorithm for
checking if two graphs are isomorphic. This construction is inductive, and
thus, can be easily applied for any interval length and Weyl group.
