Mr Zane Van de Meulen-Graaf

Honours thesis

Investigating power laws in internet AS toplogy

Investigation of Autonomous System topology has been occuring for many years, with results which are essential to improving models and hence protocol design. One of the major observational results in this field is power laws, which were originally suggested in the paper by Faloutsos et al. in 1999. Despite this paper being almost 10 years old, it continues to be referenced heavily. The major insight was that power laws connected AS degrees to their global rank, and likewise the frequency of AS degrees were linked to their degree. This changed the views of many in the modelling community, as previous models had been missing these fundamental details. Further work done by Barabasi et al. gave examples of many other complex networks in which this power-law structure is seen, and gives further reasons as to the underlying reasons why it occurs, based on the ideas of preferential connectivity. However, Crovella et al. refute many of the claims of based on the fact that the sampling implicitly preferred by real measurements contains bias, and is not actually representative of the true underlying Internet structure. The important tests used in and are both described, tested and validated in this document. From these results, it is concluded that there exists insufficient evidence for power laws, and that more work in this area is needed to truly validate the claims of.