Quantum–classical transitions in complex networks

The inherent properties of specific physical systems can be used as metaphors for investigation of the behavior of complex networks. This insight has already been put into practice in previous work, e.g., studying the network evolution in terms of phase transitions of quantum gases or representing distances among nodes as if they were particle energies. This paper shows that the emergence of different structures in complex networks, such as the scale-free and the winner-takes-all networks, can be represented in terms of a quantum–classical transition for quantum gases. In particular, we propose a model of fermionic networks that allows us to investigate the network evolution and its dependence on the system temperature. Simulations, performed in accordance with the cited model, clearly highlight the separation between classical random and winner-takes-all networks, in full correspondence with the separation between classical and quantum regions for quantum gases. We deem this model useful for the analysis of synthetic and real complex networks.

[1]  A Díaz-Guilera,et al.  Self-similar community structure in a network of human interactions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  R. Pastor-Satorras,et al.  Bosonic reaction-diffusion processes on scale-free networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  S H Strogatz,et al.  Random graph models of social networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[4]  S. Perseguers,et al.  Quantum random networks , 2009, 0907.3283.

[5]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[6]  Staša Milojević.  Power law distributions in information science: Making the case for logarithmic binning , 2010 .

[7]  T. Wassmer.  6 , 1900, EXILE.

[8]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[9]  A. Rbnyi.  ON THE EVOLUTION OF RANDOM GRAPHS , 2001 .

[10]  A. Barabasi,et al.  Bose-Einstein condensation in complex networks. , 2000, Physical review letters.

[11]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[12]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[13]  Ginestra Bianconi.  Quantum statistics in complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  B. Bollobás.  The evolution of random graphs , 1984 .

[15]  S. Adzhiev,et al.  Entropy in the sense of Boltzmann and Poincaré , 2014, Contemporary Mathematics. Fundamental Directions.

[16]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

[17]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[18]  Tuomo Hartonen,et al.  Natural networks as thermodynamic systems , 2012, Complex..

[19]  D. Saad.  Europhysics Letters , 1997 .

[20]  October I.  Physical Review Letters , 2022 .

[21]  Amin Vahdat,et al.  Hyperbolic Geometry of Complex Networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.