Tuning Topology Generators Using Spectral Distributions

Abstract

Abstract. An increasing number of synthetic topology generators are available, each claiming to produce representative Internet topologies. Every generator has its own parameters, allowing the user to generate topologies with different characteristics. However, there exist no clear guidelines on tuning the value of these parameters in order to obtain a topology with specific characteristics.In this paper we optimize the parameters of several topology generators to match a given Internet topology. The optimization is performed either with respect to the link density, or to the spectrum of the normalized Laplacian matrix. Contrary to approaches in the literature that rely only on the largest eigenvalues, we take into account the set of all eigenvalues. However, we show that on their own the eigenvalues cannot be used to construct a metric for optimizing parameters. Instead we present a weighted spectral method which simultaneously takes into account all the properties of the graph.

Weighted Spectral Distribution for Internet Topology Analysis: Theory and Applications

“…It is satisfying to note that a clear minimum exists and also that the region with low cost (Region A) lies in the scale free region as expected for a model of the Internet. Similar results were also found for the other topology generators [6].…”

“…The graph spectrum has been used for a variety of purposes in addition to characterization of Internet topologies, including space comparison [3], graph matching [4], cluster identification [5] and topology generator tuning [6]. Gkantsidis et al [7] perform a comparison of clustering coefficients using the eigenvectors of the k largest eigenvalues of the adjacency matrices of AS topologies.…”

“…These results indicates that the normalized Laplacian spectrum reveals important structural properties of the AS topology. However, as noted by Haddadi et al [6], the spectrum alone cannot be used directly to compare graphs as it contains too detailed information about the network structure. We expand on this work by demonstrating how appropriate weighting of the eigenvalues can reveal the structural differences between two topologies.…”

“…As will be seen, all the topology generators examined in this section fail to do so. For a more detailed examination of this application see Haddadi et al [6].…”

Weighted Spectral Distribution: A Metric for Structural Analysis of Networks

“…However we found this to be infeasible as generating graphs with equal numbers of links from a random model and a power-law model gives completely different outputs. For space reasons we deal with this particular issue elsewhere [18]; in this chapter we simply use the default values embedded within each generator.…”