Intuitive understanding of 'Graph Limits'

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I've been trying to understand the concept of Graph Limits (In particular, the following paper by Lovasz 'Limits of dense graph sequences') for a particular project of mine.

I'd like to know if someone could help me intuitively understand what these Graph Limits are?

Is my understanding correct when I say that, given a Graph $G = (V,E)$, if I were to 'shrink' this down into a function like $f : [0,1]^2 \to [0,1]$, then this would be some sort of representation of the limit of $G = (V,E)$?