# 📈 Graphic Schema Theory¶

Graph theory is the branch of mathematics that studies the characteristics and properties of graphs, a graph being a set of nodes or vertices that are joined by links that can be called edges or arcs and in this way relationships are represented. binaries that exist between the elements of a set.

Graphs allow us to study the interrelationships between those units that interact with each other. A clear example is how a computer network can be represented where the vertices represent the terminals while the edges represent the connections. A graph can be represented graphically as a set of vertices or nodes joined by lines. Most of the problems can be represented through a graph from the social sciences to the exact sciences.

It is important to emphasize that a graph should not be confused with graphs, since the latter have a much broader term. A graph is an ordered pair G=(V,E) where V and E are a set of vertices and edges respectively and E in turn is determined by unordered pairs of vertices {x, y} belonging to E, being adjacent x and y. In the graph they are represented by an unoriented line capable of joining these vertices. Given the case that the graph is directed, it bears the name of digraph and is denoted by the letter D, for this case (x,y) in an ordered pair that is represented by an arrow that starts from x and arrives at y, it is said that (x ,y) belongs to E.

Graph theory is based on applied and discrete mathematics, being necessary to know graphs in diverse areas such as algebra, combinatorics, polygon geometry, probability, topology and arithmetic. It is currently used to a greater extent in the field of computer science, information technology and telecommunications. Thanks to its large number of applications when it comes to optimizing processes, routes, search algorithms and flows, among others, a new theory known as network analysis is then generated.

A graph is composed of edges that are the lines capable of joining its vertices, we can classify its edges as follows:

• Adjacent edges: two edges are said to be present when they converge at the same vertex.

• Parallel Edges: Edges are said to be parallel when they share both their initial and final vertices.

• Cyclic edges: these edges start from a vertex and return to the same vertex

• Crossing: is the point where two edges intersect.

The vertices are elements that make up the graph and depending on the situation, each vertex has an associated valence corresponding to the number of edges that converge at this vertex.

The set of vertices that are interconnected by edges is called a path, it can be said that there is a path between two vertices when they are connected by an edge.

Graphs are classified into:

• Simple graph: it is the one that joins any two vertices with a single edge or it is the same to say that an edge is the only one capable of joining two specific vertices.

• Multigraph: is that graph capable of accepting more than one edge between two vertices, these edges being called loops or multiples.

• Oriented graph: as stated above, it is the directed graph or called a digraph whose edges have been given an orientation and is represented by an arrow.

Graphic Schema Theory

Graph theory is the branch of mathematics that studies the characteristics and properties of graphs, a graph being a set of nodes or vertices that are joined by links that can be called edges or arcs and in this way relationships are represented. binaries that exist between the elements of a set.

Graphs allow us to study the interrelationships between those units that interact with each other. A clear example is how a computer network can be represented where the vertices represent the terminals while the edges represent the connections. A graph can be represented graphically as a set of vertices or nodes joined by lines. Most of the problems can be represented through a graph from the social sciences to the exact sciences.

It is important to emphasize that a graph should not be confused with graphs, since the latter have a much broader term. A graph is an ordered pair G=(V,E) where V and E are a set of vertices and edges respectively and E in turn is determined by unordered pairs of vertices {x, y} belonging to E, being adjacent x and y. In the graph they are represented by an unoriented line capable of joining these vertices. Given the case that the graph is directed, it bears the name of digraph and is denoted by the letter D, for this case (x,y) in an ordered pair that is represented by an arrow that starts from x and arrives at y, it is said that (x ,y) belongs to E.

Graph theory is based on applied and discrete mathematics, being necessary to know graphs in diverse areas such as algebra, combinatorics, polygon geometry, probability, topology and arithmetic. It is currently used to a greater extent in the field of computer science, information technology and telecommunications. Thanks to its large number of applications when it comes to optimizing processes, routes, search algorithms and flows, among others, a new theory known as network analysis is then generated.

A graph is composed of edges that are the lines capable of joining its vertices, we can classify its edges as follows:

• Adjacent edges: two edges are said to be present when they converge at the same vertex.

• Parallel Edges: Edges are said to be parallel when they share both their initial and final vertices.

• Cyclic edges: these edges start from a vertex and return to the same vertex

• Crossing: is the point where two edges intersect.

The vertices are elements that make up the graph and depending on the situation, each vertex has an associated valence corresponding to the number of edges that converge at this vertex.

The set of vertices that are interconnected by edges is called a path, it can be said that there is a path between two vertices when they are connected by an edge.

Graphs are classified into:

• Simple graph: it is the one that joins any two vertices with a single edge or it is the same to say that an edge is the only one capable of joining two specific vertices.

• Multigraph: is that graph capable of accepting more than one edge between two vertices, these edges being called loops or multiples.

• Oriented graph: as stated above, it is the directed graph or called a digraph whose edges have been given an orientation and is represented by an arrow.