  We have assembled a large data-set of 613 galaxy redshifts in the Coma
cluster, the largest presently available for a cluster of galaxies. We have
defined a sample of cluster members complete to b$_{26.5}=20.0$, using a
membership criterion based on the galaxy velocity, when available, or on the
galaxy magnitude and colour, otherwise. Such a data set allows us to define
nearly complete samples within a region of 1~\Mpc\ radius, with a sufficient
number of galaxies per sample to make statistical analyses possible. Using this
sample and the {\em ROSAT} PSPC X--ray image of the cluster, we have
re-analyzed the structure and kinematics of Coma, by applying the wavelet and
adaptive kernel techniques. A striking coincidence of features is found in the
distributions of galaxies and hot intracluster gas. The two central dominant
galaxies, NGC4874 and NGC4889, are surrounded by two galaxy groups, mostly
populated with galaxies brighter than b$_{26.5}=17$ and well separated in
velocity space. On the contrary, the fainter galaxies tend to form a single
smooth structure with a central peak coinciding in position with a secondary
peak detected in X--rays, and located between the two dominant galaxies; we
suggest to identify this structure with the main body of the Coma cluster. A
continuous velocity gradient is found in the central distribution of these
faint galaxies, a probable signature of tidal interactions rather than
rotation. There is evidence for a bound population of bright galaxies around
other brightest cluster members. Altogether, the Coma cluster structure seems
to be better traced by the faint galaxy population, the bright galaxies being
located in subclusters. We discuss this evidence in terms of an ongoing
accretion of groups onto the cluster.
