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Very important is to determine, before the analysis of the term graphs, the etymological origin of it because it will allow us to know first hand the reason for its current meaning. In this way we can make it clear that that emanates from the Greek word graph, graphein, which can be translated as "record or write."

This fact is what determines, for example, that today we use this concept as an indissoluble part of other terms to which it gives that quoted meaning that is related to writing. This would be the example of a pen that is an instrument that we use to write, a graphologist who is the person who is dedicated to determine the psychological qualities of someone through the writing he performs, or the polygraph who is responsible for studying various forms of writing that are carried out secretly.

In the linguistics , a graph it is a unitary object of an abstract nature that encompasses spellings They make up a letter. The word has Greek origin and means "image" or "drawing" .

For the computer's science and the math , a graph is a graphic representation from various points that are known as nodes or vertices , which are united through lines that are called edges . By analyzing the graphs, experts get to know how reciprocal relationships develop between those units that maintain some kind of interaction.

In this sense we cannot ignore the fact that the first written document we have about what graphs are made in the eighteenth century, and more specifically in the year 1736, by Leonhard Euler. This was a mathematician and physicist, of Swiss origin, who stood out as one of the most important figures of his time in the aforementioned subject.

Specifically, the author made an article based on the bridges that exist in the city of Kaliningrad. From them, and through what is the theory of graphs, he developed an exhibition about graphs and vertices that is based on the fact that it is impossible to return to the vertex that exerts as a starting point without first going through one of the edges twice.

Graphs can be classified in various ways according to their characteristics. The graphs simple , in this sense, are those that arise when a single edge manages to join two vertices. The graphs complexes , on the other hand, they present more than one edge in union with the vertices.

On the other hand, a graph is related if you have two vertices connected through a path. What does this mean? That, for the pair of vertices (p, r), there must be some path that allows to arrive from p to r.

Instead, a graph is strongly connected if the pair of vertices has a connection through at least two different paths.

A simple graph can also be full if the edges are able to join all the pairs of vertices, while a graph is bipartite if its vertices arise by the union of a pair of sets of vertices and if a series of conditions is fulfilled.

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