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arXiv · 0712.2349

Optimization and Scale-freeness for Complex Networks

Petter Minnhagen·Sebastian Bernhardsson
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Abstract

Complex networks are mapped to a model of boxes and balls where the balls are distinguishable. It is shown that the scale-free size distribution of boxes maximizes the information associated with the boxes provided configurations including boxes containing a finite fraction of the total amount of balls are excluded. It is conjectured that for a connected network with only links between different nodes, the nodes with a finite fraction of links are effectively suppressed. It is hence suggested that for such networks the scale-free node-size distribution maximizes the information encoded on the nodes. The noise associated with the size distributions is also obtained from a maximum entropy principle. Finally explicit predictions from our least bias approach are found to be born out by metabolic networks.

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Petter Minnhagen, Sebastian Bernhardsson. 2007-12-14. Optimization and Scale-freeness for Complex Networks. https://doi.org/10.1063/1.2720101

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