  The Brownian net, which has recently been introduced by Sun and Swart [SS08],
and independently by Newman, Ravishankar and Schertzer [NRS08], generalizes the
Brownian web by allowing branching. In this paper, we study the structure of
the Brownian net in more detail. In particular, we give an almost sure
classification of each point in $R^2$ according to the configuration of the
Brownian net paths entering and leaving the point. Along the way, we establish
various other structural properties of the Brownian net.
