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Open AccessArticle

Network Decomposition and Complexity Measures: An Information Geometrical Approach

Sony Computer Science Laboratories, inc. Takanawa muse bldg. 3F, 3-14-13, Higashi Gotanda, Shinagawa-ku, Tokyo 141-0022, Japan
Entropy 2014, 16(7), 4132-4167; https://doi.org/10.3390/e16074132
Received: 28 March 2014 / Revised: 24 June 2014 / Accepted: 14 July 2014 / Published: 23 July 2014
(This article belongs to the Special Issue Information Geometry)
We consider the graph representation of the stochastic model with n binary variables, and develop an information theoretical framework to measure the degree of statistical association existing between subsystems as well as the ones represented by each edge of the graph representation. Besides, we consider the novel measures of complexity with respect to the system decompositionability, by introducing the geometric product of Kullback–Leibler (KL-) divergence. The novel complexity measures satisfy the boundary condition of vanishing at the limit of completely random and ordered state, and also with the existence of independent subsystem of any size. Such complexity measures based on the geometric means are relevant to the heterogeneity of dependencies between subsystems, and the amount of information propagation shared entirely in the system. View Full-Text
Keywords: information geometry; complexity measure; complex network; system decompositionability; geometric mean information geometry; complexity measure; complex network; system decompositionability; geometric mean
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MDPI and ACS Style

Funabashi, M. Network Decomposition and Complexity Measures: An Information Geometrical Approach. Entropy 2014, 16, 4132-4167. https://doi.org/10.3390/e16074132

AMA Style

Funabashi M. Network Decomposition and Complexity Measures: An Information Geometrical Approach. Entropy. 2014; 16(7):4132-4167. https://doi.org/10.3390/e16074132

Chicago/Turabian Style

Funabashi, Masatoshi. 2014. "Network Decomposition and Complexity Measures: An Information Geometrical Approach" Entropy 16, no. 7: 4132-4167. https://doi.org/10.3390/e16074132

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