Row-column visibility graph approach to two-dimensional landscapes

doi:10.1088/1674-1056/23/7/078904

Abstract A new concept, called the row-column visibility graph, is proposed to map two-dimensional landscapes to complex networks. A cluster coverage is introduced to describe the extensive property of node clusters on a Euclidean lattice. Graphs mapped from fractals generated with the probability redistribution model behave scale-free. They have pattern-induced hierarchical organizations and comparatively much more extensive structures. The scale-free exponent has a negative correlation with the Hurst exponent, however, there is no deterministic relation between them. Graphs for fractals generated with the midpoint displacement model are exponential networks. When the Hurst exponent is large enough (e.g., H>0.5), the degree distribution decays much more slowly, the average coverage becomes significant large, and the initially hierarchical structure at H<0.5 is destroyed completely. Hence, the row-column visibility graph can be used to detect the pattern-related new characteristics of two-dimensional landscapes.

Keywords: row-column visibility graph landscape roughness

Received: 27 December 2013
Revised: 02 January 2014
Accepted manuscript online:

PACS:	89.75.Hc	(Networks and genealogical trees)
	72.15.Rn	(Localization effects (Anderson or weak localization))
	05.50.+q	(Lattice theory and statistics)
	05.45.Df	(Fractals)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10975099), the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, China, the Innovation Program of Shanghai Municipal Education Commission, China (Grant No. 13YZ072), the Shanghai Leading Discipline Project, China (Grant No. XTKX2012), and the Innovation Fund Project for Graduate Students of Shanghai, China (Grant No. JWCXSL1302).

Corresponding Authors: Yang Hui-Jie
E-mail: hjyang@ustc.edu.cn

About author: 89.75.Hc; 72.15.Rn; 05.50.+q; 05.45.Df

Cite this article:

Xiao Qin (肖琴), Pan Xue (潘雪), Li Xin-Li (李信利), Mutua Stephen, Yang Hui-Jie (杨会杰), Jiang Yan (蒋艳), Wang Jian-Yong (王建勇), Zhang Qing-Jun (张庆军) Row-column visibility graph approach to two-dimensional landscapes 2014 Chin. Phys. B 23 078904

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Row-column visibility graph approach to two-dimensional landscapes

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