biostudies-literatureWilliams OEZonMwMinistry of Economy and Competitiveness | Agencia Estatal de InvestigaciónRCUK | Engineering and Physical Sciences Research CouncilEngineering and Physical Sciences Research Council499https://www.ebi.ac.uk/biostudies/studies/S-EPMC8789900biostudies-literatureUnknown13(1)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 richNature communicationsThe shape of memory in temporal networks.PMC8789900EP/N013492/1EP/P01660X/1MDM-2017-071195105006Millan APWilliams OELatora VLacasa LfalseThe shape of memory in temporal networks.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 rich2022-01-01T00:00:00Z2022 Jan2025-04-04T08:41:02.253Z2025-04-04T08:41:02.253ZS-EPMC87899003507899010.1038/s41467-022-28123-z