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Methods and Applications of Algorithmic ComplexityApplications to Graph and Network Complexity

Methods and Applications of Algorithmic Complexity: Applications to Graph and Network Complexity [We show that numerical approximations of Kolmogorov complexity of graphs and networks capture some group-theoretic and topological properties of empirical networks, ranging from metabolic to social networks, and of small synthetic networks that we have produced. That K and the size of the group of automorphisms of a graph are correlated opens up interesting connections to problems in computational geometry, and thus connects several measures and concepts from complexity science. We derive these results via two different Kolmogorov complexity approximation methods applied to the adjacency matrices of the graphs and networks. The methods used are the traditional lossless compression approach to Kolmogorov complexity, and the normalised version of the Block Decomposition Method (Chap. 6) based on algorithmic probability theory.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Methods and Applications of Algorithmic ComplexityApplications to Graph and Network Complexity

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Publisher
Springer Berlin Heidelberg
Copyright
© Springer-Verlag GmbH Germany, part of Springer Nature 2022
ISBN
978-3-662-64983-1
Pages
165 –189
DOI
10.1007/978-3-662-64985-5_8
Publisher site
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Abstract

[We show that numerical approximations of Kolmogorov complexity of graphs and networks capture some group-theoretic and topological properties of empirical networks, ranging from metabolic to social networks, and of small synthetic networks that we have produced. That K and the size of the group of automorphisms of a graph are correlated opens up interesting connections to problems in computational geometry, and thus connects several measures and concepts from complexity science. We derive these results via two different Kolmogorov complexity approximation methods applied to the adjacency matrices of the graphs and networks. The methods used are the traditional lossless compression approach to Kolmogorov complexity, and the normalised version of the Block Decomposition Method (Chap. 6) based on algorithmic probability theory.]

Published: May 17, 2022

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