A small-world network derived from the deterministic uniform recursive tree

As the deterministic version of the uniform recursive tree (URT), the deterministic uniform recursive tree (DURT) has been intensively studied by Zhang et al. (2008) [21]. They gave several important properties of DURT, including its topological characteristics and spectral properties. Although DURT shows a logarithmic scaling with the size of the network, DURT is not a small-world network since its clustering coefficient is zero. In this paper, we propose a new deterministic small-world network by adding some edges with a simple rule in each DURT iteration, and then give the analytic solutions to several topological characteristics of the model proposed.