## The mean number of vertices in small connected components of random geometric graphs

I place $N$ points on a circular plane of radius $R$, and draw edges to connect points that are less than or equal to some distance $D$ to form a set of graphs or cliques $G_i$. As a function of $N$, $R$, and $D$, what is the mean number of points, $m_k$, that participate in graphs with $k$ or fewer vertices?

To clarify, the $N$ points are randomly placed on the circular plane with uniform probability across its surface.

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 I've rephrased your title to simplify it a bit - see en.wikipedia.org/wiki/Random_geometric_graph . Feel free to revert it if I have misread your question. – jc Feb 15 2012 at 16:04 @jc Thanks for the new title suggestion, I like it. – EclipseInterlude Feb 15 2012 at 16:09