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 NRAO VLA Sky Survey 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). 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. This provides new insights into their nature. 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 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. This enabled us to compare key physical properties of their active galactic nuclei, such as the black hole mass, spin, Eddington ratio, jet kinetic power, total radio power, magnetic field, and size. We find that GRGs in high-excitation state statistically have larger sizes, stronger radio power, jet kinetic power, and higher Eddington ratio than those in low-excitation state. Our analysis reveals a strong correlation between the black hole Eddington ratio 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. The probability of finding the brightest cluster galaxy as a GRG is quite low and even lower for high-mass clusters. 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.

Tables A1-A4 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/642/A153