We study the effect of massive neutrinos on the formation and evolution of the first filaments containing the first star-forming halos of mass M \sim 10 ^ { 6 } M _ { \odot } at z \sim 20 .
With the help of the extended Press-Schechter formalism , we evaluate analytically the rates of merging of the first star-forming halos into zero-dimensional larger halos and one-dimensional first filaments .
It is shown that as the neutrino mass fraction f _ { \nu } increases , the halo-to-filament merging rate increases while the halo-to-halo merging rate decreases sharply .
For f _ { \nu } \leq 0.04 , the halo-to-filament merging rate is negligibly low at all filament mass scales , while for f _ { \nu } \geq 0.07 the halo-to-filament merging rate exceeds 0.1 at the characteristic filament mass scale of \sim 10 ^ { 9 } M _ { \odot } .
The distribution of the redshifts at which the first filaments ultimately collapse along their longest axes is derived and found to have a sharp maximum at z \sim 8 .
We also investigate the formation and evolution of the second generation filaments which contain the first galaxies of mass 10 ^ { 9 } M _ { \odot } at z = 8 as the parent of the first generation filaments .
A similar trend is found : For f _ { \nu } \geq 0.07 the rate of clustering of the first galaxies into the second-generation filaments exceeds 0.3 at the characteristic mass scale of \sim 10 ^ { 11 } M _ { \odot } .
The longest-axis collapse of these second-generation filaments are found to occur at z \sim 3 .
The implications of our results on the formation of massive high- z galaxies and the early metal enrichment of the intergalactic media by supernova-driven outflows , and possibility of constraining the neutrino mass from the mass distribution of the high- z central blackholes are discussed .