Picture of person typing on laptop with programming code visible on the laptop screen

World class computing and information science research at Strathclyde...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by researchers from the Department of Computer & Information Sciences involved in mathematically structured programming, similarity and metric search, computer security, software systems, combinatronics and digital health.

The Department also includes the iSchool Research Group, which performs leading research into socio-technical phenomena and topics such as information retrieval and information seeking behaviour.


A matrix perturbation view of the small world phenomenon

Higham, Desmond J. (2007) A matrix perturbation view of the small world phenomenon. SIAM Review, 49 (1). pp. 91-108. ISSN 0036-1445

Full text not available in this repository. Request a copy from the Strathclyde author


We use techniques from applied matrix analysis to study small world cutoff in a Markov chain. Our model consists of a periodic random walk plus uniform jumps. This has a direct interpretation as a teleporting random walk, of the type used by search engines to locate web pages, on a simple ring network. More loosely, the model may be regarded as an analogue of the original small world network of Watts and Strogatz [Nature, 393 (1998), pp. 440-442]. We measure the small world property by expressing the mean hitting time, averaged over all states, in terms of the expected number of shortcuts per random walk. This average mean hitting time is equivalent to the expected number of steps between a pair of states chosen uniformly at random. The analysis involves nonstandard matrix perturbation theory and the results come with rigorous and sharp asymptotic error estimates. Although developed in a different context, the resulting cutoff diagram agrees closely with that arising from the mean-field network theory of Newman, Moore, and Watts [Phys. Rev. Lett., 84 (2000), pp. 3201-3204].