The Π Sequence As a Complex Network

In this paper, a new topological approach for studying a sufficiently long random number sequence is proposed. By segmenting the sequence into groups of digits which represent the node identities while the undirected edges symbolize the adjacency between them, a network is constructed for analysis. In particular, the network constructed from a π sequence is examined in detail and its properties are contrasted with the Erdos–Renyi (ER) random graph model. Based on the observation that there are more nodes with even degrees than the adjacent odd counterparts in the constructed network, a new random graph model named Random Eulerian (RE) model and its extension are finally proposed and analyzed.