Statistical and Machine Learning Approaches for Network Analysis

6.7 Generating Topologies with Optimum Parameters

Table 6.3 displays the optimum values for the topology generators for generating networks that are close to the Skitter graph. In addition, we give the values for C₃(θ), which show that PFP gives the closest fit followed by BA, GLP, Waxman, and finally Inet. While these results are mostly expected, the ranking of Inet as the worst topology generator is surprising. We have also listed some of the default parameters used in certain generators such as BRITE [28]. While many of the optimized parameters are close to the default values, which is encouraging, it should be noted that the default parameters are for a typical graph and are not selected for any particular situation. Thus, a direct comparison is meaningless.

Table 6.3 Optimum Parameter Values for Matching Skitter Topology.

Figure 6.17a shows the weighted spectra for each of the topology generators and inspection of the figure goes some way to explaining the discrepancy in the results. As can be seen the main peak in the weighted spectra for the Skitter data occurs at a value of λ = 0.4. The Waxman generator peak occurs at λ = 0.6 which is closer to 1 demonstrating the greater amount of random structure in the Waxman topologies. However, for the Inet generator the peak occurs at the correct point (λ = 0.4) but the weighted power at this point is far greater than in the Skitter ...