The European Physical Journal Special Topics

, Volume 222, Issue 6, pp 1389–1401 | Cite as

Towards understanding the behavior of physical systems using information theory

  • Rick QuaxEmail author
  • Andrea Apolloni
  • Peter M. A. Sloot
Regular Article Information Theory of Dynamic Networks


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.


Social Network European Physical Journal Special Topic Degree Distribution Scale Free Network State Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  • Rick Quax
    • 1
    Email author
  • Andrea Apolloni
    • 2
  • Peter M. A. Sloot
    • 1
    • 3
    • 4
  1. 1.Computational ScienceUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.I.S.I. FoundationTurinItaly
  3. 3.National Research University of Information Technologies, Mechanics and Optics (ITMO)Saint PetersburgRussia
  4. 4.Nanyang Technological UniversitySingaporeSingapore

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