Graphs and Graph Theory – an Introduction - Learning Neo4j - page 5

To summarize, a graph is nothing more than an abstract, mathematical
representation of two or more entities, which are somehow connected or related
to each other. Graphs model pairwise relations between objects. They are, therefore,
always made up of the following components:
• The nodes of the graph, usually representing the objects mentioned
previously : In math, we usually refer to these structures as vertices; but
for this topic, and in the context of graph databases such as Neo4j, we will
always refer to vertices as nodes.
• The links between the nodes of the graph : In math, we refer to these
structures as edges, but again, for the purpose of this topic, we will refer
to these links as relationships.
• The structure of how nodes and relationships are connected to each other
makes a graph : Many important qualities, such as the number of edges
connected to a node, what we referred to as degree, can be assessed. Many
other such indicators also exist.
Now that we have graphs and understand a bit more about their nature and history,
it's time to look at the discipline that was created on top of these concepts, often
referred to as the graph theory.
Deinition and usage of graph theory
When Euler inventedtheirstgraph,hewastryingtosolveaveryspeciicproblem
ofthecitizensofKönigsberg,withaveryspeciicrepresentation/modelandavery
speciicalgorithm.Itturnsoutthattherearequiteafewproblemsthatcanbe:
• Described using the graph metaphor of objects and pairwise relations
between these objects
• Solved by applying a mathematical algorithm to this structure
Themechanismisthesame,andthescientiicdisciplinethatstudiesthesemodeling
and solution patterns, using graphs, is often referred to as the graph theory, and it
is considered to be a part of discrete Mathematics.