Research on degree correlations of the Thue–Morse hierarchical network

Abstract

In this paper, we construct a hierarchical network generated from the Thue–Morse sequence. First, we deduce that the degree distribution of the Thue–Morse hierarchical network follows an exponential distribution. Then, we compute the degree correlations by calculating the average degree of all neighbors of nodes which have degree k, denoted [Formula: see text]. By getting an accurate range of [Formula: see text], we show that [Formula: see text] and the Thue–Morse hierarchical network is assortative. Finally, we conclude that the hierarchical networks generated from substitution sequences still have the same properties as deterministic hierarchical networks.