Analysing a Dendrogram to find parent and ancestor nodes (genealogy)

I have the output Z from a linkage algorithm in MATLAB. I am trying to find the genealogy of the internal nodes and leaves of the dendrogram. The genealogy is defined as the ordered set of of internal nodes connecting leaf i (internal node α_h) to the root α_1. I also want to be able to find the parent node - this is the node w of v in which w immediately precedes v on the path from the root to v. Would anyone be willing to explain how I can do this using MATLAB?

In case my definitions weren't clear enough, an example case is shown in the image.

The genealogy of leaf 3 is G(3)={α_7, α_2, α_1} and the genealogy of internal node α_7 is G(α_7)={α_7, α_2, α_1}. An example for the parents: the parent node of α_7 is α_2, which I denote as g(α_2)=α_7.

I hope now it's clearer as to what I want the code to find and do using the input of Z. Your help is much appreciated!