  The formation of supermassive black holes (SMBHs) in the Universe and its
role in the properties of the galaxies is one of the open questions in
astrophysics and cosmology. Though, traditionally, electromagnetic waves have
been instrumental in direct measurements of SMBHs, significantly influencing
our comprehension of galaxy formation, gravitational waves (GW) bring an
independent avenue to detect numerous binary SMBHs in the observable Universe
in the nano-Hertz range using the pulsar timing array observation. This brings
a new way to understand the connection between the formation of binary SMBHs
and galaxy formation if we can connect theoretical models with multi-messenger
observations namely GW data and galaxy surveys. Along these lines, we present
here the first paper on this series based on {\sc Romulus25} cosmological
simulation on the properties of the host galaxies of SMBHs and propose on how
this can be used to connect with observations of nano-Hertz GW signal and
galaxy surveys. We show that the most dominant contribution to the background
will arise from sources with high chirp masses which are likely to reside in
low redshift early-type galaxies with high stellar mass, largely old stellar
population, and low star formation rate, and that reside at centers of galaxy
groups and manifest evidence of recent mergers. The masses of the sources show
a correlation with the halo mass and stellar mass of the host galaxies. This
theoretical study will help in understanding the host properties of the GW
sources and can help in establishing a connection with observations.
