### Information Theoretic Approach to Social Networks

#### Abstract

**Abstract. **We propose an information theoretic model for sociological networks. The model is a micro canonical ensemble of states and particles. The states are the possible pairs of nodes (i.e. people, sites and alike) which exchange information. The particles are the energetic information bits. With analogy to bosons gas, we define for these networks’ model: entropy, volume, pressure and temperature. We show that these definitions are consistent with Carnot efficiency (the second law) and ideal gas law. Therefore, if we have two large networks: hot and cold having temperatures T_{H} and T_{C }and we remove Q energetic bits from the hot network to the cold network we can save W profit bits. The profit will be calculated from W< Q (1-T_{H}/T_{C}), namely, Carnot formula. In addition it is shown that when two of these networks are merged the entropy increases. This explains the tendency of economic and social networks to merge.

**Keywords: **Social networks, Economic networks, Information theory.

**JEL. **C62.

#### Keywords

#### References

Barabási, A.L., & Réka, A. (1999). Emergence of scaling in random networks, *Science*, 286(5439), 509-512. doi. 10.1126/science.286.5439.509

Barabási, A.L., & Frangos, J. (2002). *Linked: The New Science of Networks*. Perseus Books Group: New York.

Barabási, A.L., & Oltvai, Z. (2004). Network bioloy, *Nature Reviews Genetics,* 5, 101-113. doi. 10.1038/nrg1272

Erdős, P., & Rényi, A. (1959). On random graphs. *Publicationes Mathematicae, *6, 290–297.

Kafri, O. (2009). The distributions in nature and entropy principle. [Retrieved from].

Kafri, O. (2014). Follow the Multitude - A Thermodynamic Approach. *Natural Science*, 6, 528-531. doi. 10.4236/ns.2014.67051

Kafri, O., & Kafri, H. (2013). *Entropy - God’s dice game, *CreateSpace, pp. 208-210. [Retrieved from].

Planck, M. (1901). Über das Gesetz der Energieverteilungim Normalspectrum. *Annalen der Physik*, 309(3), 553-563. doi. 10.1002/andp.19013090310

Shannon, C.E. (1948). A mathematical theory of communication. *Bell System Technical Journal*, 27(3), 379–423. doi. 10.1002/j.1538-7305.1948.tb01338.x

DOI: http://dx.doi.org/10.1453/jest.v4i1.1162

### Refbacks

- There are currently no refbacks.

Journal of Economic and Social Thought - J. Econ. Soc. Thoug. - JEST - **www.kspjournals.org**

ISSN: 2149-0422. Editor : **editor-jest@kspjournals.org** Secretarial: **secretarial@kspjournals.org ** Istanbul - Turkey.

Copyright © KSP Journals