  After four years of data taking, the IceCube neutrino telescope has detected
54 high-energy starting events (HESE, or contained-vertex events) with
deposited energies above 20TeV. They represent the first ever detection of
high-energy extraterrestrial neutrinos and therefore, the first step in
neutrino astronomy. In order to study the energy, flavor and isotropy of the
astrophysical neutrino flux arriving at Earth, we perform different analyses of
two different deposited energy intervals, [10 TeV $-$ 10 PeV] and [60 TeV $-$
10 PeV]. We first consider an isotropic unbroken power-law spectrum and
constrain its shape, normalization and flavor composition. Our results are in
agreement with the preliminary IceCube results, although we obtain a slightly
softer spectrum. We also find that current data are not sensitive to a possible
neutrino-antineutrino asymmetry in the astrophysical flux. Then, we show that
although a two-component power-law model leads to a slightly better fit, it
does not represent a significant improvement with respect to a single power-law
flux. Finally, we analyze the possible existence of a North-South asymmetry,
hinted at by the combination of the HESE sample with the through-going muon
data. If only using HESE data, the scarce statistics from the northern
hemisphere does not allow us to reach any conclusive answer, which indicates
that the HESE sample alone is not driving the potential North-South asymmetry.
