This chapter begins with a definition of what a graph is. While the definition is rather abstract, it is general enough to make graph theory relevant and applicable to a wide range of systems, in a variety of contexts. We will also see how to represent graphs in Python (or any other programming language). Such a representation allows a computerized inspection of many graph properties, as well as implementing various algorithms on graphs. By the end of this chapter, you will be familiar with many basic notions in this field. The last two sections of this chapter introduce the notions of clusters and clustering, and of hierarchical clustering in the context of phylogenetic trees. We note that the treatment of these two topics here hardly touches their surface – both are deep subjects in their own right, covered by vast and diverse literature.