Network Decomposition and Complexity Measures: An Information Geometrical Approach

Entropy

关键词: information geometry;    complexity measure;    complex network;    system decompositionability;    geometric mean;   

DOI  :  10.3390/e16074132

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland