Randomness criteria in binary visibility graph and complex network perspective

We introduce the binary visibility graph (BVG) for mapping random binary sequences into complex networks. Several topological aspects of the constructed graphs, such as degree distribution, clustering coefficient, and mean visibility length have been thoroughly investigated. Our simulations on the probability distributions for four sample random binary sequences (RBS) confirm the reliability of the BVG for RBS analysis. Moreover, we propose the topological properties of the graph as a randomness criteria. In this way, we have presented some possible randomness tests using BVG. A comparison has been made between these tests and National Institute of Standards and Technology (NIST) tests on four samples and the results are promising. These tests can distinguish between weak and strong RBSs.