Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/31131
Title: Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes
Authors: Heitzig, J
Donges, JF
Zou, Y
Marwan, N
Kurths, J
Keywords: Interdisciplinary Physics
Issue Date: 2012
Publisher: Springer
Source: European physical journal. B, Condensed matter and complex systems, 2012, v. 85, no. 1, 38 How to cite?
Journal: European physical journal. B, Condensed matter and complex systems 
Abstract: When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or infinite region or set of objects of interest. The selection procedure, e.g., formation of a subset or some kind of discretization or aggregation, typically results in individual nodes of the studied network representing quite differently sized parts of the domain of interest. This heterogeneity may induce substantial bias and artifacts in derived network statistics. To avoid this bias, we propose an axiomatic scheme based on the idea of node splitting invariance to derive consistently weighted variants of various commonly used statistical network measures. The practical relevance and applicability of our approach is demonstrated for a number of example networks from different fields of research, and is shown to be of fundamental importance in particular in the study of spatially embedded functional networks derived from time series as studied in, e.g., neuroscience and climatology.
URI: http://hdl.handle.net/10397/31131
ISSN: 1434-6028
EISSN: 1434-6036
DOI: 10.1140/epjb/e2011-20678-7
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