The shape of memory in temporal networks

Oliver E. Williams, Lucas Lacasa*, Ana P. Millán, Vito Latora*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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.
Original languageEnglish
Article number499
JournalNature Communications
Issue number1
Publication statusPublished - 1 Dec 2022

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