Complex networks constructed from irrational number sequences

In this paper, we construct (d, r) networks from sequences of different irrational numbers. In detail, segment an irrational number sequence of length M into groups of d digits which represent the nodes while two consecutive groups overlap by r digits (r = 0,1,...,d-1), and the undirected edges indicate the adjacency between two consecutive groups. (3, r) and (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 d, r and even sequence length M 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.

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The authors wish to thank the anonymous reviewer for the helpful comments and suggestions. This work is supported in part by the Chinese National Natural Science Foundation (Grant Nos. 70771084, 60804039, and 60974081), in part by the National Basic Research 973 Program of China under Grant No. 2007CB310805, and in part by the Doctoral Fund of Ministry of Education of China under Grant No. 200804861072.

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The authors wish to thank the anonymous reviewer for the helpful comments and suggestions. This work is supported in part by the Chinese National Natural Science Foundation (Grant Nos. 70771084, 60804039, and 60974081), in part by the National Basic Research 973 Program of China under Grant No. 2007CB310805, and in part by the Doctoral Fund of Ministry of Education of China under Grant No. 200804861072.