The visibility graph of n-bonacci sequence

Abstract

In this paper, we study both the visibility graph and horizontal visibility graph of n-bonacci sequence. Firstly, we map Fibonacci sequence to complex network by using visibility graph algorithm, and its degree sequence is related to some combinatorial properties of words. Then, we study the visibility graph degree distribution of n-bonacci sequence by coding words. We obtain that its degree distribution is between the exponential and power-law distributions. On the other hand, the horizontal visibility graph sequences of n-bonacci sequence over different alphabets correspond to the same n-bonacci sequence, and its degree distribution tends to exponential distribution as n→∞. Finally, we explain the reason why fractal sequences are mapped into scale-free networks.