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I'm reading these lecture notes and I am confused about the use of the phrase "natural operator" and "natural quadratic" on page three.

While the adjacency matrix is the most natural matrix to associate with a graph, I also find it the least useful. Eigenvalues and eigenvectors are most meaningful when used to understand a natural operator or a natural quadratic form. The adjacency matrix provides neither.

Can someone explain to me what these phrases mean? Does "natural" refer to $\mathbb{N}$?

Union Boss
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    It has shades of the technical meaning from category theory, but I guess it is something looser than this: roughly speaking, "making no arbitrary choices." – Qiaochu Yuan May 23 '13 at 02:11
  • What text can I read to develop some understanding or intuition about this word? Can be at the undergraduate or (if necessary) the graduate level. Any category theory text? – Union Boss May 23 '13 at 02:14
  • I would ignore it for now. The understanding will come gradually. – Qiaochu Yuan May 23 '13 at 02:17

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