This chapter explains how to incorporate the information obtained from graphs and dendrograms into the portfolio optimization process. Graphs have gained the attention of academics and practitioners since the seminal works of Mantegna (Eur Phys J B 11(1):193–197, 1999) and Tumminello et al. (Proc Natl Acad Sci 102(30):10421–10426, 2005) that show how the most representative relationships among assets can be represented through graphs like the minimum spanning tree and the triangulated maximally filtered graph, respectively. Graphs can be used to increase the diversification of investment portfolios through the addition of constraints on the absolute and relative position of the assets in the graph. On the other hand, dendrograms allow us to identify assets with similar behavior and we can use this information to diversify investment portfolios through the addition of constraints to invest only in assets that belong to different clusters.