  Given a graph property $\mathcal{P}$, it is interesting to determine the
typical structure of graphs that satisfy $\mathcal{P}$. In this paper, we
consider monotone properties, that is, properties that are closed under taking
subgraphs. Using results from the theory of graph limits, we show that if
$\mathcal{P}$ is a monotone property and $r$ is the largest integer for which
every $r$-colorable graph satisfies $\mathcal{P}$, then almost every graph with
$\mathcal{P}$ is close to being a balanced $r$-partite graph.
