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Entropy 2014, 16(7), 4132-4167; doi:10.3390/e16074132
Article

Network Decomposition and Complexity Measures: An Information Geometrical Approach

Received: 28 March 2014; in revised form: 24 June 2014 / Accepted: 14 July 2014 / Published: 23 July 2014
(This article belongs to the Special Issue Information Geometry)
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Abstract: 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.
Keywords: information geometry; complexity measure; complex network; system decompositionability; geometric mean information geometry; complexity measure; complex network; system decompositionability; geometric mean
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Funabashi, M. Network Decomposition and Complexity Measures: An Information Geometrical Approach. Entropy 2014, 16, 4132-4167.

AMA Style

Funabashi M. Network Decomposition and Complexity Measures: An Information Geometrical Approach. Entropy. 2014; 16(7):4132-4167.

Chicago/Turabian Style

Funabashi, Masatoshi. 2014. "Network Decomposition and Complexity Measures: An Information Geometrical Approach." Entropy 16, no. 7: 4132-4167.


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