  We have performed first-principle calculations of the electronic structure
and exchange couplings for the nanotube compound Na$_{2}$V$_{3}$O$_{7}$ using
the LDA+U approach. Our results show that while the intra-ring exchange
interactions are mainly antiferromagnetic, the inter-ring couplings are {\it
ferromagnetic}. We argue that this is a consequence of the strong hybridization
between filled and vacant 3d vanadium orbitals due to the low symmetry of
Na$_{2}$V$_{3}$O$_{7}$, which results into strong - and often dominant -
ferromagnetic contributions to the total exchange interaction between vanadium
atoms. A comparison with results of previous works is included.
