The Analytical Solution of the Average Distance for Delayed Deterministic Recursive Trees

Abstract

On the basis of the recursive trees, we propose a kind of delayed recursive trees with the feature that not all the existing nodes produce new nodes in each evolving step. Using the solutions of difference equation, the analytical expression of the average distance is obtained. This family of delayed recursive trees exhibits small-world characteristics. In addition, the average distance of this delayed trees is smaller than that of the recursive trees.