A graphical representation is a graphic or topological representation of a mathematical or conceptual structure of a certain complexity. In a graphic representation, each entity of the structure is assigned a geometric object (point, node, arrow, ...) and the relationships between objects are presented through geometric distances, arrows or other graphic entities.

Graph of a function

That is, for every element there is a single element such that or in more conventional notation. The subset is called the "graph" of the function and can be represented in the plane as the graph of a function.

Graph theory

The set of possible states of a system and the states accessible from a given state can be represented by a directed graph. Furthermore, some aspects related to flows or specificities of the transition from one state to another can be represented by a labeled directed graph (see figure).

Simple Lie algebras

The classification of simple Lie algebras was completed at the beginning of the century, thanks to the efforts of Wilhelm Killing and Élie Cartan, later Eugene Dynkin devised a very useful graphical representation that allowed us to understand the internal structure of all possible simple Lie algebras. Each connected Dynkin diagram presents a simple Lie algebra, in which the circles represent the "roots" of the algebra and the lines the relationships between them.