Can Graph Theory Exist Without Visual Graphs?

AI Thread Summary
Graph theory can exist without visual representations, as its foundational definitions focus on set relationships rather than pictorial elements. While some argue that modern mathematics increasingly favors algebraic approaches over visual aids, others contend that contemporary textbooks incorporate more graphs than ever. The debate highlights a tension between abstract mathematical concepts and the utility of visual aids in understanding. Despite the possibility of studying graph theory without diagrams, many find that visual representations enhance comprehension. Ultimately, the role of visuals in graph theory remains a contentious topic in the mathematical community.
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From the definition of a graph, it dosen't mention anything about a pictorial graph. Things are only dealt with set wise so it is possible to do graph theory without graphs? It would be extremely unnatural though.
 
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Yes it is possible to do graph theory without pictures. Modern mathematics has a desire to take things away from pictures and move it into algebra, which is a shame really. Entire textbooks go without a single diagram these days...
 
Gib Z said:
Yes it is possible to do graph theory without pictures. Modern mathematics has a desire to take things away from pictures and move it into algebra, which is a shame really. Entire textbooks go without a single diagram these days...

I find it the opposite, I think that modern mathematics is growing more pictorial. Now every single explanation has a graph to go with it, and textbooks usually more graphs than ever, since the theory is more developed, with new aspects on calculus etc.
 
Gib Z said:
Yes it is possible to do graph theory without pictures. Modern mathematics has a desire to take things away from pictures and move it into algebra, which is a shame really. Entire textbooks go without a single diagram these days...

Have you done graph theory with pictures?
 
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