  Fuzzy dark matter (FDM) is a promising candidate for dark matter,
characterized by its ultra-light mass, which gives rise to wave effects at
astrophysical scales. These effects offer potential solutions to the
small-scale issues encountered within the standard cold dark matter (CDM)
paradigm. In this paper, we investigate the large-scale structure of the cosmic
web using FDM simulations, comparing them to CDM-only simulations and a
simulation incorporating baryonic effects. Our study employs the nearest
neighbor (NN) analysis as a new statistical tool for examining the structure
and statistics of the cosmic web in an FDM universe. This analysis could
capture the information absent in the two-point correlation functions. In
particular, we analyze data related to the spherical contact, nearest neighbor
distances, and the angle between the first and second nearest neighbors of
halos. Specifically, we utilize probability distribution functions, statistical
moments, and fitting parameters, as well as G(x), F(x), and J(x) functions to
analyze the above data. Remarkably, the results from the FDM simulations differ
significantly from the others across these analyses, while no noticeable
distinction is observed between the baryonic and CDM-only simulations.
Moreover, the lower FDM mass leads to more significant deviations from the CDM
simulations. These compelling results highlight the efficiency of the NN
analysis - mainly through the use of the J(x) function, $s_3$, $l_{3}$ and
$a_4$ parameters - as a prominent new tool for investigating FDM on large
scales and making observational predictions.
