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.