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This paper explores how the network structure of local inter-industry labour flows relates to regional economic resilience across 72 local labour markets in Sweden. Drawing on recent advancements in network science we stress-test these networks against the sequential elimination of their nodes, finding substantial heterogeneity in network robustness across regions. Regression analysis with LASSO selection in the context of the 2008 crisis indicates that labour flow network robustness is a prominent structural predictor of employment change during crisis. These findings elaborate on how variation in the self-organisation of regional economies as complex systems makes for more or less resilient regions.