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Graphs don't have vectors, spaces do. A space is just an n-dimensional "graph". Vectors written in columns next to each other are matrices. Matrices can describe transformation of space, and if the transformation is linear (straight lines stay straight) there will be some vectors that stay the same (unaffected by the transformation). These are called eigenvectors.
Thanks for the response! Honestly wasn't expecting any. I understand what you're saying as a pure student would, but could you explain what you mean by "a space is a just an n-dimensional graph"?
Would the vertices map to some coordinate in space? Or am I completely misunderstanding.
I misunderstood a little, I assumed a function graph, which could be R^n space. But for the graph-theory-graphs (sets of vertices and edges) it's similar, you can model the graph using adjacency matrix (NxN matrix for a graph of N vertices, where the vertices 'mapped' to a row and column by index. Usually consisting of real numbers representing distance between the "row" and "column" node) and look at it from the linear algebra point of view. That allows to model some characteristics of the graph. But honestly I haven't mixed these two fields of maths much, so I hope what I wrote is somewhat understandable.