  Two power series models are proposed to represent self-similarity and they
are compared to the Zipf and Benford distributions. Since evolution of a social
network is associated with replicating self-similarity at many levels, the
nature of interconnections can serve as a measure of the optimality of its
organization. In contrast with the Zipf distribution where the middle term is
the harmonic mean of the adjoining terms, our distribution considers the middle
term to be the geometric mean. In one of the power series models, the scaling
factor at one level is shown to be the golden ratio. A model for evolution of
networks by oscillations between two different self-similarity measures is
described.
