The set of all eigenvalues of a characteristic matrix of a graph, also referred to as the spectrum, is a well-known topology retrieval method. In this paper, we study the spectrum of the Laplacian matrix of an observable part of the internet graph at the IP-level, extracted from traceroute measurements performed via RIPE NSS and PlanetLab. In order to investigate the factors influencing the Laplacian spectrum of the observed graphs, we study the following complex network models: the random graph of Erdos-Renyi, the smallworld of watts and strogatz and the scale-free graph, derived from a Havel-Hakimi powerlaw degree sequence. Along with these complex network models, we also study the corresponding minimum spanning tree (MST). Extensive simulations show that the Laplacian spectra of complex network models differ substantially from the spectra of the observed graphs. However, the Laplacian spectra of the MST in the Erdos-Renyi random graph with uniformly distributed link weights does bear resemblance to it. Furthermore, we discuss an extensive set of topological charateristics extracted from the Laplacian spectra of the observed real-world graphs as well as from complex network models.@en

In this paper we study the spectral radius of a number of real-life networks. This study is motivated by the fact that the smaller the spectral radius, the hight the robustness of a network agianst the spread of viruses. First we study how well-known upper bounds for the spectral radius of graphs match to the spectral radii of the social network of the Dutch soccer team, the Dutch roadmap network, the network of the observable part of the Internet graph at the IP-level and teh Autonomous System level. Secondly, we compare the spectral radius for these real-life networks with those of commonly used complex network models.@en

In this paper we study an example of a complex network, namely the road infrastructure of the Netherlands. In order to investigate the factors influencing the robustness of the complex network under consideration, we calculate a set of generic topological characteristics, related to the connectivity, degree, clustering and the shortest path length. Along with these widely considered topological characteristics, we also study the spectrum of the road graph, i.e. the collection of all eigenvalues of the assiciated adjacency matrix and the Laplacian matrix. The topological characteristics show that the road infrastructure differs substantially from many other real-world networks. However, there a complex structures, as for instance the power grid, that resemble topological properties of the Dutch road infrastructure.@en