Visibility graph analysis of geophysical time series: Potentials and possible pitfalls

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Abstract

Recently, complex network approaches to time series analysis have been developed and successfully applied to geophysical records. In this paper, the visibility graph approach is re-considered, which has been found useful as an alternative tool for describing the fractal properties of a time series. The interpretation of various graph-theoretical measures in the context of visibility graphs, their mutual interdependence, and their sensitivity in the presence of missing values and uncertainties (posing typical challenges in geophysical time series analysis) are thoroughly discussed. The obtained results are illustrated for some exemplary records from different fields of geosciences.

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The structure and function of complex networks

M. Newman (2003)

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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Statistical mechanics of complex networks

Reka Albert, Albert-László Barabási (2001)

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.

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Error and attack tolerance of complex networks

Albert-László Barabási, Hawoong Jeong, Reka Albert (2000)

Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. In this paper we demonstrate that error tolerance is not shared by all redundant systems, but it is displayed only by a class of inhomogeneously wired networks, called scale-free networks. We find that scale-free networks, describing a number of systems, such as the World Wide Web, Internet, social networks or a cell, display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected by even unrealistically high failure rates. However, error tolerance comes at a high price: these networks are extremely vulnerable to attacks, i.e. to the selection and removal of a few nodes that play the most important role in assuring the network's connectivity.