A wide range of complex networks can be described by characterising the connections and dependencies that exist between the individual components within them. A study, ‘The Emergence of Informative Higher Scales in Complex Networks’, published in the open access journal Complexity shows how relationships between nodes can be studied.
In the process, the authors Brennan Klein and research assistant professor Erik Hoel, of Northeastern University and Tufts University, USA, respectively, devise a measure known as ‘effective information’ for networks and describe its behaviour in common examples of such systems.
The results could be of particular value for big data, where it is often unclear what is the best and most efficient model for a particular system.
Klein and Hoel started the project by thinking about how complex systems can be described on multiple levels and in different ways – some of which are useful and some are not. “Your computer might be described at the level of its atoms, its machine code or its operating system.
All these are valid levels that seem informative,” says Hoel. “There are also a huge number of uninformative descriptions of your computer. What separates the informative models of a system from the uninformative models, and how do different scales fit together?”
The pair found several factors that help to answer this question, including the discovery that the nodes of a system group in time as well as space, and the observation of the emergence of informativeness at macro scales. The concept of effective information could also have applications in the study of complex networks outside of computer sciences, such as biological networks. The study’s implications could reach even more diverse areas of study, Hoel suggests.
“Philosophers have long talked about the concept of ‘emergence’ but it has been a hazy and pre-theoretic one. With this sort of research focusing on how dynamics and information changes across scales, the concept of emergence might shift from a philosophical idea to a well-supported and analytic scientific one.”
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Brennan Klein and Erik Hoel, ‘The Emergence of Informative Higher Scales in Complex Networks,’ Complexity, vol. 2020, Article ID 8932526, 12 pages, 2020. https://www.hindawi.com/journals/complexity/2020/8932526/
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