  At ~50 Mpc, the Hydra I cluster of galaxies is among the closest cluster in
the z=0 Universe, and an ideal environment to study dwarf galaxy properties in
a cluster environment. We exploit deep imaging data of the Hydra I cluster to
construct a new photometric catalog of dwarf galaxies in the cluster core,
which is then used to derive properties of the Hydra I cluster dwarf galaxies
population as well as to compare with other clusters. Moreover, we investigate
the dependency of dwarf galaxy properties on their surrounding environment. The
new Hydra I dwarf catalog contains 317 galaxies with luminosity between
-18.5<$M_r$<-11.5 mag, a semi-major axis larger than ~200 pc (a=0.84 arcsec),
of which 202 are new detections, previously unknown dwarf galaxies in the Hydra
I central region. We estimate that our detection efficiency reaches 50% at the
limiting magnitude $M_r$=-11.5 mag, and at the mean effective surface
brightness $\overline{\mu}_{e,r}$=26.5 mag/$arcsec^2$. We present the standard
scaling relations for dwarf galaxies and compare them with other nearby
clusters. We find that there are no observational differences for dwarfs
scaling relations in clusters of different sizes. We study the spatial
distribution of galaxies, finding evidence for the presence of substructures
within half the virial radius. We also find that mid- and high-luminosity
dwarfs ($M_r$<-14.5 mag) become on average redder toward the cluster center,
and that they have a mild increase in $R_e$ with increasing clustercentric
distance, similar to what is observed for the Fornax cluster. No clear
clustercentric trends are reported with surface brightness and S\'ersic index.
Considering galaxies in the same magnitude-bins, we find that for high and
mid-luminosity dwarfs ($M_r$<-13.5 mag) the g-r color is redder for the
brighter surface brightness and higher S\'ersic n index objects.
