Fixed point limits of self-similar network sequences

The aim of this paper is to focus on the fixed point limits of growing self-similar networks. The results are interpreted on the generalized form of the scale-free network analyzed by Barabási, Ravasz and Vicsek. We base our paper on weighted graph edit distances defined on these networks.

We base our paper on sets of growing network sequences with the corresponding parametrized weighted graph edit distances. As the main result, it is showed that the iterated function systems corresponding to the self-similar networks has unique fixed points.

Thus, our results highlight a new connection between the fields of networks science and fixed point theory.