  We present the first results of a project called SAGAN, which is dedicated
solely to the studies of relatively rare megaparsec-scale radio galaxies in the
Universe, called giant radio galaxies (GRGs). We have identified 162 new GRGs
primarily from the NVSS with sizes ranging from ~0.71 Mpc to 2.82 Mpc in the
redshift range of ~0.03 - 0.95, of which 23 are hosted by quasars (giant radio
quasars, GRQs). As part of the project SAGAN, we have created a database of all
known GRGs, the GRG catalogue, from the literature (including our new sample);
it includes 820 sources. For the first time, we present the multi-wavelength
properties of the largest sample of GRGs. Our results establish that the
distributions of the radio spectral index and the black hole mass of GRGs do
not differ from the corresponding distributions of normal-sized radio galaxies
(RGs). However, GRGs have a lower Eddington ratio (ER) than RGs. Using the
mid-infrared data, we classified GRGs in terms of their accretion mode: either
a high-power radiatively efficient high-excitation state, or a radiatively
inefficient low-excitation state. We find that GRGs in high-excitation state
statistically have larger sizes, stronger radio power, jet kinetic power, and
higher ER than those in low-excitation state. Our analysis reveals a strong
correlation between the ER and the scaled jet kinetic power, which suggests a
disc-jet coupling. Our environmental study reveals that ~10% of all GRGs may
reside at the centres of galaxy clusters, in a denser galactic environment,
while the majority appears to reside in a sparse environment. We find that the
probability of BCG as a GRG is quite low. We present new results for GRGs that
range from black hole mass to large-scale environment properties. We discuss
their formation and growth scenarios, highlighting the key physical factors
that cause them to reach their gigantic size. Abridged.
