  Galaxies congregate in clusters and along filaments, and are missing from
large regions referred to as voids. These structures are seen in maps derived
from spectroscopic surveys that reveal networks of structure that are
interconnected with no clear boundaries. Extended regions with a high
concentration of galaxies are called 'superclusters', although this term is not
precise. There is, however, another way to analyse the structure. If the
distance to each galaxy from Earth is directly measured, then the peculiar
velocity can be derived from the subtraction of the mean cosmic expansion, the
product of distance times the Hubble constant, from observed velocity. The
peculiar velocity is the line-of-sight departure from the cosmic expansion and
arises from gravitational perturbations; a map of peculiar velocities can be
translated into a map of the distribution of matter. Here we report a map of
structure made using a catalogue of peculiar velocities. We find locations
where peculiar velocity flows diverge, as water does at watershed divides, and
we trace the surface of divergent points that surrounds us. Within the volume
enclosed by this surface, the motions of galaxies are inward after removal of
the mean cosmic expansion and long range flows. We define a supercluster to be
the volume within such a surface, and so we are defining the extent of our home
supercluster, which we call Laniakea. A key component of this paper is an
accompanying movie that can be viewed (also in 3D) and downloaded at
http://irfu.cea.fr/laniakea or http://vimeo.com/pomarede/laniakea
