This article aims at showing an application of graph theory to the description of the syntactic relations between words in English. Graph theory is part of Network Science, a new and compelling branch of mathematics that has undergone huge development over the past 20 years. The linguistic theoretical background is the Lexicon Grammar (LG) that in turn is built on the ground of the Harrisian grammar for operators and arguments. Graph theory is particularly useful in order to show how sentences have underlying structures that can be visualized through the use of graphs, and whose properties can be measured and quantified with the typical mathematical tools used by the researchers in the field of Network Science. A graph is a set of nodes (also called ‘vertices’) and links (also called ‘edges’); the links connect the nodes. Each sentence will be described as a graph, in which the words have to be seen as the nodes and the syntactic relations between the words are the links.