Random directed acyclic graphs (DAGs) based on imposing an order on Erdős-Rényi and scale free random graphs are widely used for evaluating causal discovery algorithms. We show that in such DAGs, the set of nodes reachable via open paths, termed relatives, increases monotonically along the causal order. We assess the prevalence of this pattern numerically, and demonstrate that it can be exploited for causal order recovery via sorting by the estimated number of relatives. We note that many simulations in the literature feature settings where this yields an excellent proxy for the causal order, and show that a strict increase of relatives along the causal order leads to a singular Markov equivalence class. We propose sampling time-series DAGs as a possible alternative and discuss implications for causal discovery algorithms and their evaluation on synthetic data.

翻译：基于对埃尔迪斯-雷尼图和尺度无关随机图施加顺序的随机有向无环图（DAG）被广泛用于评估因果发现算法。我们证明，在此类DAG中，通过开放路径可达的节点集（称为亲缘集）沿因果顺序单调递增。我们通过数值分析评估了该模式的普遍性，并证明可通过按亲缘集估计数量排序来利用此模式恢复因果顺序。我们注意到，许多文献中的仿真实验设置了使得该排序成为因果顺序优良近似的情形，并证明沿因果顺序的亲缘集严格递增会导致奇异马尔可夫等价类。我们提出采样时间序列DAG作为可能的替代方案，并讨论了对因果发现算法及其在合成数据上评估的启示。