Horizontal visibility graphs mapped from multifractal trinomial measures.

In this paper, we study the horizontal visibility graphs mapped from multifractal trinomial measures, which are determined by three parameters, p 1 , p 2 , and p 3 , where 0 < p 1 < p 2 < p 3 < 1 , p 1 + p 2 + p 3 = 1. First, we regard multifractal trinomial measures as time series and map them into horizontal visibility graphs. Then, we study the degree distributions in the three cases of p 1 p 3 = p 2 2 , p 1 p 3 > p 2 2 , and p 1 p 3 < p 2 2 . Due to the self-similarity of the induced graphs, the degree distributions of the series are derived using an iterative method. And the numerical simulations coincide excellently with the theoretical degree distributions. • HVGs mapped from multifractal trinomial measures are studied. • Degree distributions of HVGs are derived in an iterative method. • The numerical results obtained support the theoretical analysis. [ABSTRACT FROM AUTHOR]