  Astrophysical neutrino events have been measured in the last couple of years,
which show an isotropic distribution, and the current discussion is their
astrophysical origin. We use both isotropic and anisotropic components of the
diffuse neutrino data to constrain the contribution of a broad number of
extra-galactic source populations to the observed neutrino sky. We simulate
up-going muon neutrino events by applying statistical distributions for the
flux of extragalactic sources, and by Monte Carlo method we exploit the
simulation for current and future IceCube, IceCube-Gen2 and KM3NeT exposures.
We aim at constraining source populations by studying their angular patterns,
for which we assess the angular power spectrum. We leave the characteristic
number of sources ($N_{\star}$) as a free parameter, which is roughly the
number of neutrino sources over which the measured intensity is divided. With
existing two-year IceCube data, we can already constrain very rare, bright
sources with $N_{\star}\lesssim$100. This can be improved to $N_{\star}\lesssim
10^4$-$10^5$ with IceCube-Gen2 and KM3NeT with ten-year exposure, constraining
the contribution of BL Lacs ($N_{\star}=6\times10^{2}$). On the other hand, we
can constrain weak sources with large number densities, like starburst galaxies
($N_{\star} = 10^{7}$), if we measure an anisotropic neutrino sky with future
observations.

High Energy Astrophysical Phenomena;Cosmology and Nongalactic Astrophysics