Information Theoretic Approach to Social Networks

TL;DR

This paper introduces an information theoretic model for social networks, applying thermodynamic concepts like entropy and temperature to analyze information exchange and network merging behaviors.

Contribution

It develops a novel thermodynamic framework for social networks, linking physical principles to sociological phenomena and explaining network merging through entropy increase.

Findings

Networks obey Carnot efficiency in information transfer

Entropy increases upon network merging

Thermodynamic analogy explains social network behaviors

Abstract

We propose an information theoretic model for sociological networks. The model is a microcanonical 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 TH and TC 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 equal or smaller than Q (1-TH/TC), 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.