  We compare the spatial clustering and physical properties of the active
galactic nuclei (AGN) and star-forming galaxies (SFG) at fixed stellar mass
using a volume limited sample from the Sloan Digital Sky Survey (SDSS). The
analysis of the two-point correlation function shows that the AGN are more
strongly clustered than the SFG. The closer proximity to the $5^{th}$ nearest
neighbour for the AGN than that for the SFG indicates that AGN prefer the
denser regions. We compare the distributions of the $(u-r)$ colour, star
formation rate (SFR), D$4000$ and concentration index of the AGN and SFG after
matching their stellar mass distributions. The null hypothesis can be rejected
at $>99.99\%$ confidence level in each case. The comparisons are also carried
out at different densities. The differences persist at the same significance
level in both the high and low density regions, implying that such differences
do not originate from the variations in the density. Alternatively stated, the
AGN activity can be triggered in both the high and low density regions. An
analysis of the correlations between the different physical properties at fixed
stellar mass reveals that the anticorrelations of SFR with morphology, colour
and recent star formation history are $2-3$ times stronger for the AGN than for
the SFG. It suggests that the presence of a bulge and the availability of gas
are the two most crucial requirements for AGN activity. We propose a picture
where the galaxies at fixed stellar mass may have widely different assembly
histories, leading to significant variations in bulge properties and cold gas
content. Whether a galaxy of a given stellar mass can acquire the suitable
conditions for AGN activity remains uncertain due to a broad diversity of
assembly history. We conclude that AGN are stochastic phenomena owing to an
underlying role of the assembly bias.
