System expandability becomes a major concern for highly parallel computers and data centers, because their number of nodes gradually increases year by year. In this context we propose a low-degree topology and its floor layout in which a cabinet or node set can be newly inserted by connecting short cables to a single existing cabinet. Our graph analysis shows that the proposed topology has low diameter, low average shortest path length and short average cable length comparable to existing topologies with the same degree. When incrementally adding nodes and cabinets to the proposed topology, its diameter and average shortest path length increase modestly. Our discrete-event simulation results show that the proposed topology provides a comparable performance to 2-D Torus for some parallel applications. The network cost and power consumption of DSN-F modestly increase when compared to the counterpart non-random topologies.

Many deterministic small-world network models have been proposed so far, and they have been proven useful in describing some real-life networks which have fixed interconnections. Search efficiency is an important property to characterize small-world networks. This paper tries to clarify how the search procedure behaves when random walks are performed on small-world networks, including the classic WS small-world network and three deterministic small-world network models: the deterministic small-world network created by edge iterations, the tree-structured deterministic small-world network, and the small-world network derived from the deterministic uniform recursive tree. Detailed experiments are carried out to test the search efficiency of various small-world networks with regard to three different types of random walks. From the results, we conclude that the stochastic model outperforms the deterministic ones in terms of average search steps.

Using daily infection data for Hong Kong we explore the validity of a variety of models of disease propagation when applied to the SARS epidemic. Surrogate data methods show that simple random models are insufficient and that the standard epidemic susceptible-infected-removed model does not fully account for the underlying variability in the observed data. As an alternative, we consider a more complex small world network model and show that such a structure can be applied to reliably produce simulations quantitative similar to the true data. The small world network model not only captures the apparently random fluctuation in the reported data, but can also reproduce mini-outbreaks such as those caused by so-called "super-spreaders" and in the Hong Kong housing estate of Amoy Gardens.