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Motivated by the detection of cascades of defaults in economy, we developed adetection framework for an endogenous spreading based on causal motifs wedefine in this paper. We assume that the change of state of a vertex can betriggered by an endogenous or an exogenous event, that the underlying networkis directed and that times when vertices changed their states are available. Inaddition to the data of company defaults, we also simulate cascades driven bydifferent stochastic processes on different synthetic networks. We show thatsome of the smallest motifs can robustly detect endogenous spreading events.Finally, we apply the method to the data of defaults of Croatian companies andobserve the time window in which an endogenous cascade was likely happening.

Causal motifs and existence of endogenous cascades in directed networks with application to company defaults