Graph Theory: Pure or Applied?

[andlook]

Hi

Is graph theory a more pure or applied subject?

I thought it was pure but now I am confusing myself because it has so many applications.

Thanks

 

[TheMadman]

It is both a theoretical and applied subject. You will decide how you'll use it. You can construct proofs and/or you can experiment with numerous graphs, their properties and their application. but a theoretical background is a must

 

[Werg22]

I'd say pure. When I took graph theory, it was all about proving stuff about graphs (which is far from easy!).

 

[epenguin]

I have dabbled in it both for fascination of 'pure' aspects and for some applications.

Would it be useful to classify it not by, or not only by, the pure/applied axis but along the concrete/abstract axis. It no doubt has abstract aspects, but it is often about perfectly 'concretely' visualisable things, whether they are useful or not and they always might be - a bit like 2 and 3D Euclidean geometry. Is that not one nice thing about it - for some of us?

Is not another nice aspect that it is relatively independent of other branches of mathematics, so a beginner can go quite far without a vast mathematical background?

 

[CellCoree]

for your question. Graph theory is a branch of mathematics that deals with the study of graphs, which are mathematical structures used to model relationships between objects. It has both pure and applied aspects, and the distinction between the two can be somewhat blurred.

On one hand, graph theory is a pure mathematical subject, meaning that it is primarily concerned with the development and exploration of abstract concepts and theories. This includes topics such as graph coloring, graph connectivity, and graph algorithms, which have no direct practical applications but are important for understanding the underlying principles of graph theory.

On the other hand, graph theory also has numerous practical applications in various fields such as computer science, operations research, and social network analysis. For example, graph algorithms are used to optimize network traffic, while social network analysis relies on graph theory to study the structure and dynamics of social networks. In these cases, graph theory is considered an applied subject, as it is being used to solve real-world problems.

In summary, graph theory can be seen as both pure and applied, depending on the context and the specific topics being studied. Ultimately, the distinction between the two is not as important as the fact that graph theory has a wide range of applications and continues to be a valuable tool for solving complex problems in various fields.