Many real-world domains are relational in nature since they consist of a set of objects related to each other in complex ways. However, there are also flat data sets and if we want to apply graph-based algorithms, it is necessary to construct a graph from this data. This paper aims to: i) increase the exploration of graph-based algorithms and ii) proposes new techniques for graph construction from flat data. Our proposal focuses on constructing graphs using link prediction measures for predicting the existence of links between entities from an initial graph. Starting from a basic graph structure such as a minimum spanning tree, we apply a link prediction measure to add new edges in the graph. The link prediction measures considered here are based on structural similarity of the graph that improves the graph connectivity. We evaluate our proposal for graph construction in supervised and semi-supervised classification and we confirm the graphs achieve better accuracy.