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Let G be a graph with undirected and directed edges. Its representation isgiven by assigning a vector space to each vertex, a bilinear form on thecorresponding vector spaces to each directed edge, and a linear map to eachdirected edge. Two representations A and A' of G are called isomorphic if thereis a system of linear bijections between the vector spaces corresponding to thesame vertices that transforms A to A'. We prove that if two representations areisomorphic and close to each other, then their isomorphism can be chosen closeto the identity.

Lipschitz property for systems of linear mappings and bilinear forms