For an $n$-vertex graph $G$, we say it is a sparse graph if $e(G)=o(n^2)$. Otherwise if $e(G)=\theta (n^2)$, we say it is a dense graph.
For a sequence of dense graphs $G_1,G_2,\dots,$ we know that it converges to a graphon(bounded measurable symmetric function $[0,1]^2\to [0,1]$). (Large networks and graph limits, Lovasz.)
For a sequence of sparse graphs $G_1,G_2,\dots,$ how could we describe its limit? If we use graphon, isn't it $0$ graphon since $\lim o(n^2)/n^2=0$?
So how to understand sparse graph limits and what paper or textbook is good for learning sparse graph limits?
