This is the representation I usually see used for the tree of nodes for skinning 3D models. There each node has a transform, and the most common operation is to recompute the world transform for all nodes, formed by composing the transform for each node with the one for all of its parents. If the array is sorted so that parents always precede their children, that's just a straight loop over the arrays

   for i = 0, num_nodes do
     if parents[i] == -1 then
       world_xforms[i] = xforms[i]
     else
       world_xforms[i] = world_xforms[parents[i]] * xforms[i]