Abstract
Network science has made great progress in the study of binary relationships between pairs of elements. Although it has been known for decades that n-ary are ubiquitous in complex systems, progress in this area has been much slower. A condensed account is given of the family of network structures which includes graphs, networks, multilevel networks and multiplex networks for binary relations, and hypergraphs, simplices complexes and hypernetworks for n-ary relations. These structures are naturally integrated in a generalising framework. This family of network structures supports a new theory of multilevel systems where structures at one level become vertices at higher levels through part-whole aggregation interleaved with taxonomic aggregation. Although the structures presented are necessary to understand the dynamics of complex multilevel systems, there are many open questions. These are presented for consideration by the network community.
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Supported by the UK Home Office and HEFCE through a Police Knowledge Fund grant to the Open University National Centre for Policing Research and Professional Development.
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Johnson, J.H. (2017). Open Questions in Multidimensional Multilevel Network Science. In: Shmueli, E., Barzel, B., Puzis, R. (eds) 3rd International Winter School and Conference on Network Science . NetSci-X 2017. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-55471-6_10
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DOI: https://doi.org/10.1007/978-3-319-55471-6_10
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