Statistical and Machine Learning Approaches for Network Analysis

6.5 Comparing Topology Generators

Most past comparisons of topology generators have been limited to the average node degree, the node degree distribution and the joint degree distribution. The rationale for choosing these metrics is that if those properties are closely reproduced then the value of other metrics will also be closely reproduced [33].

In this section, we show that current topology generators are able to match first and second order properties well, that is, average node degree and node degree distribution, but fail to match many other topological metrics. We also discuss the importance of various metrics in our analysis.¹⁶

6.5.1 Methodology

For each generator, we specify the required number of nodes and generate 10 topologies of that size to provide confidence intervals for the metrics. We then compute the metrics introduced in Section 6.4 on both the generated and observed AS topologies. All topologies studied in this chapter are undirected, preventing us from considering peering policies and provider–customer relationships. This limitation is forced upon us by the design of the generators as they do not take such policies into account.

Each topology generator uses several parameters, all of which could be tuned to best fit a particular size of topology. However, there are two problems with attempting this tuning. First, doing so requires selecting an appropriate goodness-of-fit measure, of which there are many as noted in Section 6.4. Second, in any case tuning ...