I am having trouble transforming a maximum weighted spanning tree into a directed tree such that each node is allowed at most one parent node. Taken from page 141 Friedman et. al (1997), the outline of the algorithm is as follows:
1) Compute $I_{\hat{P}_{D}}(X_{i};X_{j})$ between each pair of variables $i \neq j$ where $$I_{\hat{P}_{D}}(X_{i};X_{j}) = \sum_{x,y} P(x,y) log\left(\frac{P(x,y)}{P(x)P(y)}\right)$$ 2) Build a complete undirected graph in which the vertices are the variables in $X$. Annotate the weight of an edge connecting $X_{i}$ to $X_{j}$ by $$I_{\hat{P}_{D}}(X_{i};X_{j})$$ 3) Build a maximum weighted spanning tree
4) Transform the resulting undirected tree to a directed one by choosing a root variable and setting the direction of all edges to be outward from it.
I have done steps 1-3, my trouble is on step 4. As of right now I have a set of names of continuous variables $X = \{x_{1}, x_{2}, \ldots, x_{n} \}$ and a $(from , to)$ matrix of the form $$ \begin{bmatrix} x_{1}&x_{10}\\x_{3}&x_{7}\\ \vdots& \vdots \end{bmatrix} $$ For example in the undirected maximum weighted tree, there's an edge going from $x_{1}$ to $x_{10}$ and so forth (note that this could have easily been read as an edge from $x_{10}$ to $x_{1}$ because as of right now the graph is undirected). I understand exactly what's going on I'm just unsure how to actually program it. If somebody could give me a pesduocode-type overview of how I should go about implementing step 4 it would be much appreciated. If someone could provide a link to a detailed implementation of this algorithm that would be fine as well. This is my first post on stackexchange, please forgive me if I have not provided enough information or posted this question in the incorrect location.
