Euclidean Voronoi diagram of spheres in 3D has not been explored as much as it deserves even though it has significant potential impacts on diverse applications in both science and engineering. In addition, studies on the data structure for its topology have not been reported yet. Presented in this paper is the topological representation for Euclidean Voronoi diagram of spheres which is represented as a cell structure as one of typical non-manifold models. The topological representation is a variation of radial edge data structure with a consideration on the topological characteristics of Euclidean Voronoi diagram of spheres distinguished from general non-manifold models and Euclidean Voronoi diagram of points. Various topological queries in the Voronoi diagram are also presented and analyzed.