Simulation of Micro-, Grand-, and Canonical Ensembles of Complex Networks

  • Christoly Biely
  • Stefan Thurner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3993)


The analysis of statistical ensembles of networks by means of simulation is an important possibility to explore networks which emerge by optimization of some ’fitness’-function. In this paper, we compare the situations of the micro-, grand- and canonical ensemble based on their respective partition functions. We present results for a specific, recently introduced Hamiltonian. Interestingly, for all three ensembles we find scale-free networks with ’complex’ topology for a wide range of parameters. We further show results of some topological measures depending on energy and temperature.


Partition Function Degree Distribution Canonical Ensemble Statistical Ensemble Microcanonical Ensemble 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Christoly Biely
    • 1
    • 2
  • Stefan Thurner
    • 1
    • 2
  1. 1.Complex Systems Research Group, HNOMedical University of ViennaViennaAustria
  2. 2.Atominstitut der Österreichischen UniversitätenViennaAustria

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