  Two aspects of fractal networks are considered: the community structure and
the class structure, where classes of nodes appear as a consequence of a local
symmetry of nodes. The analysed systems are the networks constructed for two
selected symmetric fractals: the Sierpinski triangle and the Koch curve.
Communities are searched for by means of a set of differential equations.
Overlapping nodes which belong to two different communities are identified by
adding some noise to the initial connectivity matrix. Then, a node can be
characterized by a spectrum of probabilities of belonging to different
communities. Our main goal is that the overlapping nodes with the same spectra
belong to the same class.
