In this master's thesis we study different graph indices for two families of hierarchical trees. We recall first the construction of these graphs by using the hierarchical product of graphs on paths and stars. We name the resulting trees as hyperpaths and hyperstars. Next, we present classical communication measures on graphs and the recently introduced concept of graph communicability and some related graph indices: Wiener index, betweenness centrality, mean first passage time and Estrada index. We review known values for all these invariants in the case of hyperpaths and hyperstars, provide a combinatorial proof for their Wiener index and betweenness centrality, and compute also the communicability centrality and the Estrada index for some instances to find their dependency with the order of the tree.