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Definition (wDAG): A weighted Directed Acyclic Graph (wDAG) $\mathscr{G_{c}}$ is defined as set of ordered triplets of weights and connected random variables, such that, $k$th triplet $(w_{k}, x_{i}, x_{j})$ where by $w_{k} \in \mathbb{R}$ is the weight, an effect size, between two variates that $x_{i}$ effects $x_{j}$. There are constraints :

(ii) If there is a definition, $(w_{k}, x_{i}, x_{j})$ the reverse can't be defined, i.e., so that $(w_{k}, x_{j}, x_{i})$ does not exist.

(iii) No two causal effects sizes can't be exactly equal, $w_{k}$ can not be equal to $w_{l}$, from the same causal variable, meaning no simultaneous events caused by the same random variable. This prevents ambiguity of ordering and random tie-breaks are unnatural.

Definition (Causal Ordering from wDAG): Given $\mathscr{G_{c}}$, we can construct causal ordering among random variates $O(i)$ for $x_{i}$ using directionality and weights from $\mathscr{G_{c}}$:

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