*Complex Networks*

from the perspective of

*Statistical Physics*

The statistical physics of real-world networks,

In the past 15 years, statistical physics has been successful as a framework for modelling complex networks. On the theoretical side, this approach has unveiled a variety of physical phenomena, such as the emergence of mixed distributions and ensemble non-equivalence, that are observed in heterogeneous networks but not in homogeneous systems. At the same time, thanks to the deep connection between the principle of maximum entropy and information theory, statistical physics has led to the definition of null models for networks that reproduce features of real-world systems but that are otherwise as random as possible.Nature Reviews Physicsvolume 1, pages58–71 (2019)

#### Adjoint faculty members

#### Project Members

#### Graduated Members

Graduated date: 2019/01/10.

#### Our Papers:

** Mean-field solution of structural balance dynamics in nonzero temperature**, https://doi.org/10.1103/PhysRevE.99.062302

** Quartic Balance Theory: Global Minimum With Imbalanced Triangles, **https://arxiv.org/abs/2001.01719

### Ref:

- Romualdo Pastor-Satorras, Miguel Rubi, Albert Diaz-Guilera;
**Statistical Mechanics of Complex Networks**(Lecture Notes in Physics) - Belaza AM,
Hoefman K, Ryckebusch J, Bramson A, van den Heuvel M, Schoors K (2017)**Statistical physics of balance theory.**PLoS ONE 12(8): e0183696. - Andrea Gabrielli, Rossana Mastrandrea, Guido Caldarelli, Giulio Cimini;
**The Grand Canonical ensemble of weighted networks**, Phys. Rev. E 99, 030301 (2019) - Giulio Cimini, Tiziano Squartini, Fabio Saracco, Diego Garlaschelli, Andrea Gabrielli & Guido
Caldarelli ; **The statistical physics of real-world networks** - Bianconi, G. The entropy of randomized network ensembles.
*Europhys. Lett.***81**, 28005 (2008).**This paper derives the Boltzmann entropy of a variety of network ensembles to assess the role of structural network properties**. - Orsini, C. et al. Quantifying randomness in real networks.
*Nat. Commun.***6**, 8627 (2015).**This paper uses the**dk **-series approach to show**.that degree distributions , degree correlations and clustering often represent sufficient statistics to describe a network - Albert, R. & Barabási, A.-L. Statistical mechanics of complex networks.
*Rev. Mod. Phys0.***74**, 47–97 (2002). - Dorogovtsev, S. N., Goltsev, A. V. & Mendes, J. F. F. Critical phenomena in complex networks.
*Rev. Mod. Phys.***80**, 1275–1335 (2008). Yook , S. H., Jeong, H., Barabási, A.-L. & Tu, Y. Weighted evolving networks.*Phys. Rev. Lett.***86**, 5835–5838 (2001).- Barrat, A., Barthelemy, M. & Vespignani, A. Weighted evolving networks: coupling topology and weight dynamics.
*Phys. Rev. Lett.***92**, 228701 (2004). - Newman, M. E. J. The structure and function of complex networks.
*SIAM Rev. Soc. Ind. Appl. Math.***45**, 167–256 (2003). - Holland, P. W. & Leinhardt, S. An exponential family of probability distributions for directed graphs.
*J. Am. Stat. Assoc.***76**, 33–50 (1981).**This paper introduces ERGs as a formalism to define probability distributions for the structures of social networks**. - Park, J. & Newman, M. E. J. Statistical mechanics of networks.
*Phys. Rev. E***70**, 066117 (2004).**In this paper, ERGs are interpreted for the first time as the statistical physics framework for complex networks**. - Garlaschelli, D. & Loffredo, M. I. Generalized bose-fermi statistics and structural correlations in weighted networks.
*Phys. Rev. Lett.***102**, 038701 (2009).**This paper develops the ERG approach for a general class of weighted networks**. - Bianconi, G. Statistical mechanics of multiplex networks: entropy and overlap.
*Phys. Rev. E***87**, 062806 (2013).**This paper develops the ERG framework for multiplex networks**. - Squartini, T. & Garlaschelli, D. Analytical maximum-likelihood method to detect patterns in real networks.
*New J. Phys.***13**, 083001 (2011).**This paper turns ERGs into null models for empirically observed networks using the maximum likelihood principle**. - Jaynes, E. T. Information theory and statistical mechanics.
*Phys. Rev.***106**, 620–630 (1957).**In this milestone paper, Jaynes shows that equilibrium statistical mechanics provides an unbiased prescription to make inferences from partial information**. - Jaynes, E. T. On the rationale of maximum-entropy methods.
*Proc. IEEE***70**, 939–952 (1982).