We report small angle neutron scattering (SANS) from dilute suspensions of purified individual single wall carbon nanotubes (SWNTs) in D2O with added sodium dodecylbenzene sulfonate (NaDDBS) ionic surfactant. The scattered intensity scales as Q-1 for scattered wave vector, Q, in the range 0.005 < Q < 0.02 Å-1. The Q-1 behavior is characteristic of isolated rigid rods. A crossover of the scattered intensity power law dependence from Q-1 to Q-2 is observed at ~0.004 Å-1, suggesting the SWNTs form a loose network at 0.1 wt% with a mesh size of ~160 nm. SANS profiles from several other dispersions of SWNTs do not exhibit isolated rigid rod behavior; evidently the SWNTs in these systems are not isolated and form aggregates.