The edges of a directed acyclic graph (DAG) can be interpreted as cause-effect relations from parent to child node. Linear structural equation models (LSEM) are sets of matrices of distributions that quantify these cause-effect relations by describing a node through a linear function of its parents and some additive independent noise term. Given the LSEM of an unknown DAG, previous results have shown that the underlying DAG can only be identified up to the well-known Markov equivalence classes. Under the additional assumption that all error terms have identical variance, it has been proven that the graph can be identified uniquely. The goal of this thesis is to explore these so-called covariance equivalence classes in the general setting of an arbitrary partition of the nodes into groups with equal error variances. The main result of this thesis is the computation of covariance equivalence classes of DAGs with three and four nodes under arbitrary groups of equal error variances with the aid of the computational algebra software Macaulay2 and Maple. Based on these results, a conjecture on the case of arbitrary number of nodes that entails the two known equal error variance settings and explains the computational results is stated. Assuming that the conjecture holds true, the distribution of the sizes of covariance equivalence classes of DAGs up to six nodes is explored. Moreover, the algorithm is extended to allow cyclic graphs, however, it cannot be ensured that these results correspond to covariance equivalence classes of directed cyclic graphs. All code is available for further investigations.      «

The edges of a directed acyclic graph (DAG) can be interpreted as cause-effect relations from parent to child node. Linear structural equation models (LSEM) are sets of matrices of distributions that quantify these cause-effect relations by describing a node through a linear function of its parents and some additive independent noise term. Given the LSEM of an unknown DAG, previous results have shown that the underlying DAG can only be identified up to the well-known Markov equivalence classes....     »