Beyond Node Degree: Evaluating AS Topology Models

This is the accepted version of 'Beyond Node Degree: Evaluating AS Topology Models', archived originally at arXiv:0807.2023v1 [cs.NI] 13 July 2008.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 characterize the AS topology. Our analysis shows that, although matching degree-based properties, the existing AS topology generation models fail to capture the complexity of the local interconnection structure between ASs. Furthermore, we use BGP data from multiple vantage points to show that additional measurement locations significantly affect local structure properties, such as clustering and node centrality. Degree-based properties, however, are not notably affected by additional measurements locations. These observations are particularly valid in the core. The shortcomings of AS topology generation models stems from an underestimation of the complexity of the connectivity in the core caused by inappropriate use of BGP data

Effective graph resistance

AbstractThis paper studies an interesting graph measure that we call the effective graph resistance. The notion of effective graph resistance is derived from the field of electric circuit analysis where it is defined as the accumulated effective resistance between all pairs of vertices. The objective of the paper is twofold. First, we survey known formulae of the effective graph resistance and derive other representations as well. The derivation of new expressions is based on the analysis of the associated random walk on the graph and applies tools from Markov chain theory. This approach results in a new method to approximate the effective graph resistance. A second objective of this paper concerns the optimisation of the effective graph resistance for graphs with given number of vertices and diameter, and for optimal edge addition. A set of analytical results is described, as well as results obtained by exhaustive search. One of the foremost applications of the effective graph resistance we have in mind, is the analysis of robustness-related problems. However, with our discussion of this informative graph measure we hope to open up a wealth of possibilities of applying the effective graph resistance to all kinds of networks problems

Quantifying randomness in real networks

Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks-the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain-and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate dk-random graphs

Correlation between centrality metrics and their application to the opinion model

In recent decades, a number of centrality metrics describing network properties of nodes have been proposed to rank the importance of nodes. In order to understand the correlations between centrality metrics and to approximate a high-complexity centrality metric by a strongly correlated low-complexity metric, we first study the correlation between centrality metrics in terms of their Pearson correlation coefficient and their similarity in ranking of nodes. In addition to considering the widely used centrality metrics, we introduce a new centrality measure, the degree mass. The m order degree mass of a node is the sum of the weighted degree of the node and its neighbors no further than m hops away. We find that the B_{n}, the closeness, and the components of x_{1} are strongly correlated with the degree, the 1st-order degree mass and the 2nd-order degree mass, respectively, in both network models and real-world networks. We then theoretically prove that the Pearson correlation coefficient between x_{1} and the 2nd-order degree mass is larger than that between x_{1} and a lower order degree mass. Finally, we investigate the effect of the inflexible antagonists selected based on different centrality metrics in helping one opinion to compete with another in the inflexible antagonists opinion model. Interestingly, we find that selecting the inflexible antagonists based on the leverage, the B_{n}, or the degree is more effective in opinion-competition than using other centrality metrics in all types of networks. This observation is supported by our previous observations, i.e., that there is a strong linear correlation between the degree and the B_{n}, as well as a high centrality similarity between the leverage and the degree.Comment: 20 page

Characterization of complex networks: Application to robustness analysis

This thesis focuses on the topological characterization of complex networks. It specifically focuses on those elementary graph measures that are of interest when quantifying topology-related aspects of the robustness of complex networks. This thesis makes the following contributions to the field of complex networks. Firstly, the thesis analyses the relationships among a variety of graph measures and proposes a definite set, capable of expressing the most relevant topological properties of complex networks. Secondly, the thesis relies on spectral measures to initiate a classification of the qualitative topological properties that characterize specific classes of complex networks. Thirdly, the thesis illustrates the use of spectral measures in a quantitative characterization of topology-related aspects of the network robustness. Finally, this thesis demonstrates the use of spectral measures in a quantitative characterization of the extent to which the robustness to different types of failures manifests itself in the underlying complex networks structure.Electrical Engineering, Mathematics and Computer Scienc

Análisis de un sistema de disco parabólico con motor Stirling

Los actuales sistemas de producción de energía eléctrica presentan problemas a nivel económico, político y medioambiental. Estos problemas, lejos de disminuir, se acentúan cada año, por lo que se hace necesario encontrar nuevas formas de producción de energía. Estas nuevas formas de producción de energía eléctrica deben ser lo suficientemente efectivas como para sustituir a los sistemas basados en la quema de combustibles fósiles, además de ser respetuosas con el medio ambiente; son las denominadas energías renovables De entre las distintas tecnologías renovables, el presente documento se centró en el estudio de la energía solar termoeléctrica, y más concretamente en el estudio de los sistemas disco Stirling como sistemas de generación de energía eléctrica.Ingeniería Industria