Graph Operations and Zipfian Degree Distributions

Abstract The probability distribution on a set S = { 1, 2,..., n} defined by Pr(k) = 1/(Hnk), where Hn in the nth harmonic number, is commonly called a Zipfian distribution. In this note we look at the degree distribution of graphs created from graphs with Zipfian degree distributions using some standard graph theoretical operations. Introduction: The probability distribution on a set S = { 1, 2,..., n} defined by Pr(k) = 1/(Hnk), where Hn in the nth harmonic number, is commonly called a Zipfian distribution, after George Zipf (1902- 1950), who observed it in relation to word frequency in English. (See, for example, the discussion in [1]). Recently, it has been observed (see, e.g., [4] and [5]) tha