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Comparing graphs to determine the level of underlying structural similarity between them is a widely encountered problem in computer science. It is particularly relevant to the study of Internet topologies, such as the generation of synthetic topologies to represent the Internet's AS topology. We derive a new metric that enables exactly such a structural(More)
Comparison of graph structures is a frequently encountered problem across a number of problem domains. Comparing graphs requires a metric to discriminate which features of the graphs are considered important. The spectrum of a graph is often claimed to contain all the information within a graph, but the raw spectrum contains too much information to be(More)
Diversity is an important characterization aspect for online social networks that usually denotes the homogeneity of a network's content and structure. This paper addresses the fundamental question of diversity evolution in large-scale online communities over time. In doing so, we study different established notions of network diversity, based on paths in(More)
We introduce and study the spectral evolution model, which characterizes the growth of large networks in terms of the eigenvalue decomposition of their adjacency matrices: In large networks, changes over time result in a change of a graph's spectrum, leaving the eigenvectors unchanged. We validate this hypothesis for several large social, collaboration,(More)
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(More)
—Existing models for Internet Autonomous System (AS) topology generation make structural assumptions about the AS graph. Those assumptions typically stem from beliefs about the true properties of the Internet, e.g. hierarchy and power-laws, which arise from incorrect interpretations of incomplete observations of the AS topology. In this paper we compare AS(More)
Many models have been proposed to generate Internet Autonomous System (AS) topologies, most of which make structural assumptions about the AS graph. In this paper we compare AS topology generation models with several observed AS topologies. In contrast to most previous works, we avoid making assumptions about which topological properties are important to(More)
In this paper we study the structural evolution of the AS topology as inferred from two different datasets over a period of seven years. We use a variety of topological metrics to analyze the structural differences revealed in the AS topologies inferred from the two different datasets. In particular, to focus on the evolution of the relationship between the(More)
This paper is concerned with the case of an exogenous system in which a model is required to forecast a periodic output time series using a causal input. A novel approach is developed in which the wavelet packet transform is taken of both the dependent time series and causal input. This results in two sets of basis dictionaries and requires two bases to be(More)