We prove that p-cycles in structural equation models with an equal Gaussian variance assumption are identifiable under a certain condition. The condition is formulated with regard to the coefficient matrix. The edge weights need to have a different absolute value to ensure identifiability of the structural equation model. The partial identifiability statement is proven by analyzing the structure of the precision matrix of the structural equation model. Partial identifiability implies that different parametrizations exist yielding the same distribution. We verify this implication in a numerical experiment. In the implementation part, two structure learning algorithms for acyclic graphs are adapted for the cyclic case. Furthermore, we describe the adjustments and implement the algorithms. The two algorithms are benchmarked against an existing constraint-based approach and the outcome is analyzed. One algorithm is a basic greedy approach while the other one uses a continuous constraint to avoid simple dicycles in the nonlinear optimization of a score function. The results look promising especially for our greedy algorithm, because the algorithm can compete with the existing constraint-based approach in most of the considered dimensions. This result is particularly promising, as we attempt solving a more difficult problem by returning a directed graph.     «

We prove that p-cycles in structural equation models with an equal Gaussian variance assumption are identifiable under a certain condition. The condition is formulated with regard to the coefficient matrix. The edge weights need to have a different absolute value to ensure identifiability of the structural equation model. The partial identifiability statement is proven by analyzing the structure of the precision matrix of the structural equation model. Partial identifiability implies that differ...     »