Complex networks constructed from irrational number sequences

In this paper, we construct (d,r)(d,r) networks from sequences of different irrational numbers. In detail, segment an irrational number sequence of length MM into groups of dd digits which represent the nodes while two consecutive groups overlap by rr digits (r=0,1,…,d−1r=0,1,…,d−1), and the undirected edges indicate the adjacency between two consecutive groups. (3,r)(3,r) and (4,r)(4,r) networks are respectively constructed from 14 different irrational numbers and their topological properties are examined. By observation, we find that network topologies change with different values of dd, rr and even sequence length MM instead of the types of irrational numbers, although they share some similar features with traditional random graphs. We make a further investigation to explain these interesting phenomena and propose the identical-degree random graph model. The results presented in this paper provide some insight into distributions of irrational number digits that may help better understanding of the nature of irrational numbers.