Topological analysis of multi-node deterministic uniform recursive tree model

Deterministic uniform recursive tree (DURT) is a deterministic version of uniform recursive tree (URT). Zhongzhi Zhang et al. studied the topology and Laplace spectrum of DURT. In this paper, by changing the iterative rule of adding a single node to add multiple nodes in the process of DURT network generation, a deterministic uniform recursive tree model with multiple nodes is proposed. First of all, from the viewpoint of complex networks, we have identified the primary structure characteristics of the multi-node DURT, and provided analytical solutions corresponding to several topological characteristics. The results indicate that the network has exponential degree distribution, logarithmic growth of the average path length and assortative degree correlation.