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Psychology
Cognitive Science

The Sexual Brain

Profile image of Ray BlanchardRay Blanchard

1995, The Journal of Nervous and Mental Disease

https://doi.org/10.1097/00005053-199501000-00013
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15 pages

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Abstract

We show that numerical approximations of Kolmogorov complexity (K) 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 a normalised version of a Block Decomposition Method (BDM) based on algorithmic probability theory.

Key takeaways
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  1. Kolmogorov complexity (K) effectively captures topological properties of graphs and networks.
  2. The Block Decomposition Method (BDM) approximates K using adjacency matrices of graphs.
  3. Numerical analysis shows correlation between K and the size of automorphism groups in graphs.
  4. Real-world networks (200-1000 nodes) exhibit similar K and automorphism group size relationships as synthetic networks.
  5. Future research may explore K's behavior in larger networks and directed graphs.

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