In this article, a framework for defining and analysing a family of graphs or networks from symbolic music information is discussed. Such graphs concern different types of elements, such as pitches, chords and rhythms, and the relations among them, and are built from quantitative or categorical data contained in digital music scores. They are helpful in visualizing musical features at once, thus leading to a computational tool for understanding the general structural elements of a music fragment. Data obtained from a digital score undergoes different analytical procedures from graph and network theory, such as computing their centrality measures and entropy, and detecting their communities. We analyze pieces of music coming from different styles, and compare some of our results with conclusions from traditional music analysis techniques.