  In the inhomogeneous random graph model, each vertex $i\in\{1,\ldots,n\}$ is
assigned a weight $W_i\sim\text{Unif}(0,1)$, and an edge between any two
vertices $i,j$ is present with probability $k(W_i,W_j)/\lambda_n\in[0,1]$,
where $k$ is a positive, symmetric function and $\lambda_n$ is a scaling
parameter that controls the graph density. When $\lambda_n=1$
(resp.~$\lambda_n=O(n)$) the typical resulting graph is dense (resp.~sparse).
The goal of this paper is the study of structural properties of \textit{large}
inhomogeneous random graphs. We focus our attention on graph functions that
grow sufficiently slowly as the graph size increases. Under some additional
technical assumptions, we show that the first-order asymptotic behavior of all
such properties is the same for the inhomogeneous random graph and for the
Erd\H{o}s-R\'enyi random graph. Our proof relies on two couplings between the
inhomogeneous random graph and appropriately constructed Erd\H{o}s-R\'enyi
random graphs. We demonstrate our method by obtaining asymptotics for two
structural properties of the inhomogeneous random graph which were previously
unknown. In the sparse regime, we find the leading-order term for the chromatic
number. In the dense regime, we find the asymptotics of the so-called
$\gamma$-quasi-clique number.
