The shape of memory in temporal networks
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Williams, O.E... [et al.]. The shape of memory in temporal networks. Nat Commun 13, 499 (2022). [https://doi.org/10.1038/s41467-022-28123-z]
SponsorshipUK Research & Innovation (UKRI) Engineering & Physical Sciences Research Council (EPSRC) EP/P01660X/1; Spanish State Research Agency through the Severo Ochoa; Maria de Maeztu Program for Centers and Units of Excellence in RD MDM-2017-0711; Netherlands Organization for Health Research and Development; Dutch Epilepsy Foundation 95105006; Agencia Espanola de Investigacion (AEI) FIS2017-84256-P; La Caixa Foundation 100010434 LCF/BQ/ES15/10360004; UK Research & Innovation (UKRI); Engineering & Physical Sciences Research Council (EPSRC) EP/N013492/1; Leverhulme Trust; Spanish Government
How to best define, detect and characterize network memory, i.e. the dependence of a network’s structure on its past, is currently a matter of debate. Here we show that the memory of a temporal network is inherently multidimensional, and we introduce a mathematical framework for defining and efficiently estimating the microscopic shape of memory, which characterises how the activity of each link intertwines with the activities of all other links. We validate our methodology on a range of synthetic models, and we then study the memory shape of real-world temporal networks spanning social, technological and biological systems, finding that these networks display heterogeneous memory shapes. In particular, online and offline social networks are markedly different, with the latter showing richer memory and memory scales. Our theory also elucidates the phenomenon of emergent virtual loops and provides a novel methodology for exploring the dynamically rich structure of complex systems.