%0 Book Section %1 statphys23_0831 %A Bernhardsson, S.B. %A Minnhagen, P.M. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K complex mechanics metabolic networks scale-free statistical statphys23 topic-11 %T Scalefree Networks and Maximum Node Information %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=831 %X Our starting point is the assumption that a network structure which has evolved subject to survival of the fittest basically is organized so as to contain the maximimum number of useful distinguishable states. Our hypothesis is that the useful distinguishable states are the node information states. We develop these ideas by mapping a connected network onto a simplified model, the CDBB(Constrained Distinguishable Balls In Boxes)-model, and using a statistical mechanics formulation. The box-information state is defined as the information carried locally by the boxes. For distinguishable balls this information depends on both which specific balls goes into which box and the time order in which the specific balls arrived at a specific box: Two box information states carry the same information if there is an one-to-one mapping of boxes containing the same balls and the same relevant time-ordering. We show that the distribution of box sizes, N(k), which corresponds to the maximum box information is a scale free distribution with powerlaw index $2$. The box information is defined as $B=ln(Ømega/(Ømega_d))$ where $Ømega$ is the number of distinguishable states available and $Ømega_d$ is the degeneracy of the box-information state. The additional constraints imposed by the network topology are discussed and MC-calculation results are presented. \\\\ References:\\ P. Minnhagen, S. Bernhardsson and B.J. Kim. Scale-freeness for networks as a degenerate ground state: A Hamiltonian formulation. To appear in Europhysics letters 2007. (http://arxiv.org/abs/cond-mat/0703242). \\\\ P. Minnhagen and S. Bernhardsson. Optimization and Scale-freeness for Complex Networks. To appear in Chaos 2007.

@incollection{statphys23_0831, abstract = {Our starting point is the assumption that a network structure which has evolved subject to survival of the fittest basically is organized so as to contain the maximimum number of useful distinguishable states. Our hypothesis is that the useful distinguishable states are the node information states. We develop these ideas by mapping a connected network onto a simplified model, the CDBB(Constrained Distinguishable Balls In Boxes)-model, and using a statistical mechanics formulation. The box-information state is defined as the information carried locally by the boxes. For distinguishable balls this information depends on both which specific balls goes into which box and the time order in which the specific balls arrived at a specific box: Two box information states carry the same information if there is an one-to-one mapping of boxes containing the same balls and the same relevant time-ordering. We show that the distribution of box sizes, N(k), which corresponds to the maximum box information is a scale free distribution with powerlaw index $\gamma \geq 2$. The box information is defined as $B=ln(\Omega/(\Omega_{d}))$ where $\Omega$ is the number of distinguishable states available and $\Omega_{d}$ is the degeneracy of the box-information state. The additional constraints imposed by the network topology are discussed and MC-calculation results are presented. \\\\ References:\\ P. Minnhagen, S. Bernhardsson and B.J. Kim. Scale-freeness for networks as a degenerate ground state: A Hamiltonian formulation. To appear in Europhysics letters 2007. (http://arxiv.org/abs/cond-mat/0703242). \\\\ P. Minnhagen and S. Bernhardsson. Optimization and Scale-freeness for Complex Networks. To appear in Chaos 2007.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Bernhardsson, S.B. and Minnhagen, P.M.}, biburl = {https://www.bibsonomy.org/bibtex/2b355a23c8246152fd701ad613bbd4657/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {90f49e1770a797d3dc1bd55acaec8df0}, intrahash = {b355a23c8246152fd701ad613bbd4657}, keywords = {complex mechanics metabolic networks scale-free statistical statphys23 topic-11}, month = {9-13 July}, timestamp = {2007-06-20T10:16:30.000+0200}, title = {Scalefree Networks and Maximum Node Information}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=831}, year = 2007 }