Graph theory and definitions

Graphs are a mathematical structure composed of a set of elements, and a set of connection between them. Due to their intuitive representation, graphs are widely employed in many different fields and, in particular, in systems biology and bioinformatics. In fact, they are used to model biological networks is several case studies, but also to represent data structures in different algorithmic procedures for solving bioinformatic problems. One of the key points of this widespread adoption is also related to the strong mathematical formulation behind them. In this article, we will introduce the basic concepts of graphs, starting from their definition and the description of simple notions. We will also describe specific types of graphs, like bipartite graphs and multigraphs, and we will explain two possible representations, namely adjacency lists and adjacency matrix. Finally, we will focus on bipartite graphs, by proposing an intuitive procedure to check if a graph is bipartite.