Small-world is a common property existing in many real-life social, technological and biological networks. Small-world networks distinguish themselves from others by their high clustering coefficient and short average path length. In the past dozen years, many probabilistic small-world networks and some deterministic small-world networks have been proposed utilizing various mechanisms. In this Letter, we propose a new deterministic small-world network model by first constructing a binary-tree structure and then adding links between each pair of brother nodes and links between each grandfather node and its four grandson nodes. Furthermore, we give the analytic solutions to several topological characteristics, which shows that the proposed model is a small-world network.

Recently, the small-world network model has been popular to describe a wide range of networks such as human social relations and networks formed by biological entities. The network model achieves a small diameter with relatively few links as measured by the ratio of clustering coefficient and the number of links. It is quite natural to consider email communication similar to social network patterns. Quite surprisingly, we find from our empirical study that local email networks follow a different type of network model that falls into the category of scale-free network. We propose new network models to describe such communication structure.