Visibility graph analysis

About: Visibility graph analysis is a research topic. Over the lifetime, 111 publications have been published within this topic receiving 6100 citations. The topic is also known as: VGA.

Natural Movement: Or, Configuration and Attraction in Urban Pedestrian Movement:

Abstract: Existing theories relating patterns of pedestrian and vehicular movement to urban form characterise the problem in terms of flows to and from 'attractor' land uses. This paper contains evidence in support of a new 'configurational' paradigm in which a primary property of the form of the urban grid is to privilege certain spaces over others for through movement In this way it is suggested that the configuration of the urban grid itself is the main generator of patterns of movement. Retail land uses are then located to take advantage of the opportunities offered by the passing trade and may well act as multipliers on the basic pattern of 'natural movement' generated by the grid configuration. The configurational correlates of movement patterns are found to be measures of global properties of the grid with the 'space syntax' measure of 'integration' consistently found to be the most important. This has clear implications for urban design suggesting that if we wish to design for well used urban space, then it is not the local properties of a space that are important in the main but its configurational relations to the larger urban system.

From time series to complex networks: The visibility graph

Abstract: In this work we present a simple and fast computational method, the visibility algorithm, that converts a time series into a graph. The constructed graph inherits several properties of the series in its structure. Thereby, periodic series convert into regular graphs, and random series do so into random graphs. Moreover, fractal series convert into scale-free networks, enhancing the fact that power law degree distributions are related to fractality, something highly discussed recently. Some remarkable examples and analytical tools are outlined to test the method's reliability. Many different measures, recently developed in the complex network theory, could by means of this new approach characterize time series from a new point of view.

Space is the machine

Abstract: Since 'The social logic of space' was published in 1984, Bill Hillier and his colleagues at University College London have been conducting research on how space features in the form and functioning of buildings and cities. A key outcome is the concept of 'spatial configuration' - meaning relations which take account of other relations in a complex. New techniques have been developed and applied to a wide range of architectural and urban problems. The aim of this book is to assemble some of this work and show how it leads the way to a new type of theory of architecture: an 'analytic' theory in which understanding and design advance together. The success of configurational ideas in bringing to light the spatial logic of buildings and cities suggests that it might be possible to extend these ideas to other areas of the human sciences where problems of configuration and pattern are critical.

From Isovists to Visibility Graphs: A Methodology for the Analysis of Architectural Space

Abstract: An isovist, or viewshed, is the area in a spatial environment directly visible from a location within the space. Here we show how a set of isovists can be used to generate a graph of mutual visibility between locations. We demonstrate that this graph can also be constructed without reference to isovists and that we are in fact invoking the more general concept of a visibility graph. Using the visibility graph, we can extend both isovist and current graph-based analyses of architectural space to form a new methodology for the investigation of configurational relationships. The measurement of local and global characteristics of the graph, for each vertex or for the system as a whole, is of interest from an architectural perspective, allowing us to describe a configuration with reference to accessibility and visibility, to compare from location to location within a system, and to compare systems with different geometries. Finally we show that visibility graph properties may be closely related to manifestations of spatial perception, such as way-finding, movement, and space use.

The visibility graph: A new method for estimating the Hurst exponent of fractional Brownian motion

Abstract: Fractional Brownian motion (fBm) has been used as a theoretical framework to study real-time series appearing in diverse scientific fields. Because of its intrinsic nonstationarity and long-range dependence, its characterization via the Hurst parameter, H, requires sophisticated techniques that often yield ambiguous results. In this work we show that fBm series map into a scale-free visibility graph whose degree distribution is a function of H. Concretely, it is shown that the exponent of the power law degree distribution depends linearly on H. This also applies to fractional Gaussian noises (fGn) and generic f−β noises. Taking advantage of these facts, we propose a brand new methodology to quantify long-range dependence in these series. Its reliability is confirmed with extensive numerical simulations and analytical developments. Finally, we illustrate this method quantifying the persistent behavior of human gait dynamics.