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I suppose it depends what you mean by graph theory without linear algebra. Graphs can be represented as matrices without losing anything, so as such you can go
by karmakurtisaani 3y ago
I suppose it depends what you mean by graph theory without linear algebra. Graphs can be represented as matrices without losing anything, so as such you can go from graphs to matrices and do everything you would do with graphs alone.
For describing algorithms sticking with just the notion of graphs is convenient however, as it allows you to speak of edges, nodes, colours etc. keeping things easier to grasp.
Also, there are notions such as planar graphs which probably don't have a nice interpretation in the linear algebra point of view only.
- abdullahkhalids 3y agoI have been working with homology theory applies to planar graphs this month. A procedure for which I could not see a nice compact algorithm in just graph theory terms reduced to simple matrix multiplication with the help of homology.
- karmakurtisaani 3y agoI'm certainly not saying linear algebra is useless with planar graphs. It really depends on what is meant by graph theory vs. linear algebra here. If GT means we can fix an embedding to the space, then we have additional information such as number of crossings. However, it seems like a bit arbitrary restriction.