Running periodically traceroute-like measurements at suite frequency from a given monitor towards a fixed set of destinations allows observing a dynamics of routing topology around the monitor. This observed dynamics has revealed two main characteristics: the topology evolves at a pace much higher than expected and the occurrence of observed ip addresses provides a pattern of the ip-level routing dynamics. In this paper, we aim to provide some explanation of these characteristics through the small-world effect, observed on most complex networks. We are able to reproduce the observed dynamics by modeling the measurement on small-world graph. Thus, we show by simulation the influence of the coefficient clustering and the average path lengths on the dynamics.