2011/01/31 by J. Heitzig, Jobst Heitzig, Jonathan F. Donges +7 · 1 citation
Neuroscience · Physics and Astronomy · Psychology · #Axiom #Complex Network Analysis Techniques #Complex network #Discretization #Domain (mathematical analysis) #Functional Brain Connectivity Studies #Graph theory #Interdependent networks #Mental Health Research Topics #Node (physics) #Relevance (law) #Selection (genetic algorithm) #Set (abstract data type) #acm:05C75 #acm:05C81 #acm:05C82 #acm:90B15 #acm:91D30 #cond-mat.dis-nn #cond-mat.stat-mech #msc:05C75 #msc:05C81 #msc:05C82 #msc:90B15 #msc:91D30 #physics.data-an
paper · pdf · doi:10.1140/epjb/e2011-20678-7
published as European Physical Journal B 85, 38 (2012) · 21 pages, 13 figures
openalex publication_date 2012/01/01 · arxiv created 2012/03/22 · arxiv updated 2015/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.