The shape of memory in temporal networks Williams, Oliver E. Millán Vidal, Ana Paula L.L. acknowledges support from EPSRC ECF EP/P01660X/1 and the Spanish State Research Agency through the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in R&D (MDM-2017-0711). A.P.M. is supported by ZonMw and the Dutch Epilepsy Foundation, project number 95105006. A.P.M. acknowledges support from the Spanish Ministry of Science and Technology and the "Agencia Espanola de Investigacion (AEI)" under grant FIS2017-84256-P (FEDER funds), and from "Obra Social La Caixa" (ID 100010434 with code LCF/BQ/ES15/10360004). V.L. acknowledges support from the EPSRC project EP/N013492/1 and from the Leverhulme Trust Research Fellowship "CREATE: the network components of creativity and success". 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. 2022-02-18T11:27:38Z 2022-02-18T11:27:38Z 2022-01-25 journal article 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] http://hdl.handle.net/10481/72904 10.1038/s41467-022-28123-z eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España Nature