Structure learning in causal cyclic networks

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SAM: Structural Agnostic Model, Causal Discovery and Penalized Adversarial Learning (2018, result): “However this link is reported in a more recent model of the same authors Itani et al. (2010) that may include cycles.”
Learning linear cyclic causal models with latent variables (2012, methodology): “In these cases a cyclic model provides the natural representation, and one needs to make use of causal discovery procedures that do not rely on acyclicity (Richardson, 1996; Schmidt and Murphy, 2009; Itani et al., 2008).”
Structural Agnostic Modeling: Adversarial Learning of Causal Graphs (2018, methodology): “ to a cycle in our model and was not reported in the original consensus network of Sachs et al. (2005) supposed to be acyclic. However this link is reported in a more recent model of the same authors Itani et al. (2010) that may include cycles. 5 DISCUSSION AND EXTENSIONS We evaluated the computatio”
On Causal Discovery with Cyclic Additive Noise Models (2011, background): “Researchers have also studied cyclic causal models with discrete variables [9, 10].”