Exceptional graphs for the random walk

Random walk attachment graphs

We consider the random walk attachment graph introduced by Saramäki and Kaski and proposed as a mechanism to explain how behaviour similar to preferential attachment may appear requiring only local knowledge. We show that if the length of the random walk is fixed then the resulting graphs can have properties significantly different from those of preferential attachment graphs, and in particular...

Vertex-Reinforced Random Walk on Arbitrary Graphs

Random Walk on Directed Dynamic Graphs

Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the undirected dynamic graph model. However, realistic networks such as the ones identified above are directed. In this paper we present early work in addressing th...

Random walk with jumps in large-scale random geometric graphs

0140-3664/$ see front matter 2010 Elsevier B.V. A doi:10.1016/j.comcom.2010.01.026 q This work has been supported in part by the proje Architecture) (IST-27489), the PENED 2003 program Research and Technology (GSRT) co-financed by the and by National Sources (25%) and the NoE CONTENT * Corresponding author. Address: National and Kapo Department of Informatics and Telecommunications, I Tel.: +30...

A random walk model for infection on graphs

We address the question of understanding the effect of the underlying network topology on the spread of a virus and the dissemination of information when users are mobile performing independent random walks on a graph. To this end, we propose a simple model of infection that enables to study the coincidence time of two random walkers on an arbitrary graph. By studying the coincidence time of a ...