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Open AccessArticle

Allometric Scaling of Mutual Information in Complex Networks: A Conceptual Framework and Empirical Approach

1
Centre for Complexity Science and Department of Mathematics, Imperial College London, SW7 2AZ, London, United Kingdom
2
Institute of Innovative Research, Tokyo Institute of Technology, 4259, Nagatsuta-cho, Yokohama 226-8502, Japan
3
Department of Mathematical and Computing Science, School of Computing, Tokyo Institute of Technology, Yokohama 226-8502, Japan
4
Sony Computer Science Laboratories, 3-14-13, Higashi-Gotanda, Shinagawa-ku, Tokyo 141-0022, Japan
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2020, 22(2), 206; https://doi.org/10.3390/e22020206
Received: 20 January 2020 / Revised: 7 February 2020 / Accepted: 10 February 2020 / Published: 12 February 2020
(This article belongs to the Special Issue Complexity in Economic and Social Systems)
Complexity and information theory are two very valuable but distinct fields of research, yet sharing the same roots. Here, we develop a complexity framework inspired by the allometric scaling laws of living biological systems in order to evaluate the structural features of networks. This is done by aligning the fundamental building blocks of information theory (entropy and mutual information) with the core concepts in network science such as the preferential attachment and degree correlations. In doing so, we are able to articulate the meaning and significance of mutual information as a comparative analysis tool for network activity. When adapting and applying the framework to the specific context of the business ecosystem of Japanese firms, we are able to highlight the key structural differences and efficiency levels of the economic activities within each prefecture in Japan. Moreover, we propose a method to quantify the distance of an economic system to its efficient free market configuration by distinguishing and quantifying two particular types of mutual information, total and structural.
Keywords: complexity science, information theory, economic complexity, evolutionary dynamics, network theory complexity science, information theory, economic complexity, evolutionary dynamics, network theory
MDPI and ACS Style

Viegas, E.; Goto, H.; Kobayashi, Y.; Takayasu, M.; Takayasu, H.; Jensen, H.J. Allometric Scaling of Mutual Information in Complex Networks: A Conceptual Framework and Empirical Approach. Entropy 2020, 22, 206.

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