Causal motifs and existence of endogenous cascades in directed networks with application to company defaults
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Motivated by detection of cascades of defaults in economy, we developed a detection framework for endogenous spreading based on causal motifs we define in this paper. We assume that vertex change of state can be triggered by endogenous or exogenous event, that underlying network is directed and that times when vertices changed their states are available. In addition to data of company defaults we use, we simulate cascades driven by different stochastic processes on different synthetic networks. We also extended an approximate master equation method to directed networks with temporal stamps in order to understand in which cases detection is possible. We show that some of the smallest motifs can robustly detect cascades.
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