Definition and usage of the graph theory

When Euler invented the first graph, he was trying to solve a very specific problem of the citizens of K?nigsberg, with a very specific representation/model and a very specific algorithm. It turns out that there are quite a few problems that can be addressed as follows:

• Described using the graph metaphor of objects and pairwise relations between them
• Solved by applying a mathematical algorithm to this structure

The mechanism is the same, and the scientific discipline that studies these modeling and solution patterns, using graphs is often referred to as the graph theory and is considered to be a part of discrete mathematics.

There are lots of different types of graphs that have been analyzed in this discipline, as you can see from the following diagram:

Graph theory, the study of graph models and algorithms, has turned out to be a fascinating field of study, which has been used in many different disciplines to solve some of the most interesting questions facing mankind. Interestingly enough, it has seldom really been applied with rigor in the different fields of science that can benefit from it; maybe scientists today don't have the multidisciplinary approach required (providing expertise from graph theory and their specific field of study) to do so.

So, let's talk about some of these fields of study a bit, without giving you an exhaustive list of all applicable fields. Still, I do believe that some of these examples will be of interest for our future discussions in this book and will work up an appetite for what types of applications we will use a graph-based database, such as, Neo4j for.