Eur. Phys. J. Special Topics 222, 1389-1401 (2013)
https://doi.org/10.1140/epjst/e2013-01933-9

Regular Article

Towards understanding the behavior of physical systems using information theory

¹ Computational Science, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
² I.S.I. Foundation, 11/C Via Alassio, 10126 Turin, Italy
³ National Research University of Information Technologies, Mechanics and Optics (ITMO), Kronverkskiy 49, 197101 Saint Petersburg, Russia
⁴ Nanyang Technological University, 50 Nanyang Avenue, 639798 Singapore

^a e-mail: r.quax@uva.nl

Received: 3 June 2013
Revised: 10 July 2013
Published online: 13 September 2013

Abstract

One of the goals of complex network analysis is to identify the most influential nodes, i.e., the nodes that dictate the dynamics of other nodes. In the case of autonomous systems or transportation networks, highly connected hubs play a preeminent role in diffusing the flow of information and viruses; in contrast, in language evolution most linguistic norms come from the peripheral nodes who have only few contacts. Clearly a topological analysis of the interactions alone is not sufficient to identify the nodes that drive the state of the network. Here we show how information theory can be used to quantify how the dynamics of individual nodes propagate through a system. We interpret the state of a node as a storage of information about the state of other nodes, which is quantified in terms of Shannon information. This information is transferred through interactions and lost due to noise, and we calculate how far it can travel through a network. We apply this concept to a model of opinion formation in a complex social network to calculate the impact of each node by measuring how long its opinion is remembered by the network. Counter-intuitively we find that the dynamics of opinions are not determined by the hubs or peripheral nodes, but rather by nodes with an intermediate connectivity.