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A {\em string graph} is the intersection graph of a family of continuous arcsin the plane. The intersection graph of a family of plane convex sets is astring graph, but not all string graphs can be obtained in this way. We provethe following structure theorem conjectured by Janson and Uzzell: The vertexset of {\em almost all} string graphs on $n$ vertices can be partitioned into{\em five} cliques such that some pair of them is not connected by any edge($n\rightarrow\infty$). We also show that every graph with the above propertyis an intersection graph of plane convex sets. As a corollary, we obtain that{\em almost all} string graphs on $n$ vertices are intersection graphs of planeconvex sets.

Almost all string graphs are intersection graphs of plane convex sets