  We revisit the filamentary structures of galaxies around the Virgo cluster,
exploiting a larger dataset based on the HyperLeda database than previous
studies. In particular, this includes a large number of low-luminosity
galaxies, resulting in better sampled individual structures. We confirm seven
known structures in the distance range 4~$h^{-1}$~Mpc~$<$ SGY~$<$ 16~$h^{-1}$
Mpc, now identified as filaments, where SGY is the axis of the supergalactic
coordinate system roughly along the line of sight. The Hubble diagram of the
filament galaxies suggests they are infalling toward the main-body of the Virgo
cluster. We propose that the collinear distribution of giant elliptical
galaxies along the fundamental axis of the Virgo cluster is smoothly connected
to two of these filaments (Leo~II~A and B). Behind the Virgo cluster
(16~$h^{-1}$~Mpc~$<$ SGY~$<$ 27~$h^{-1}$~Mpc), we also identify a new filament
elongated toward the NGC 5353/4 group ("NGC 5353/4 filament") and confirm a
sheet that includes galaxies from the W and M clouds of the Virgo cluster ("W-M
sheet"). In the Hubble diagram, the NGC 5353/4 filament galaxies show infall
toward the NGC 5353/4 group, whereas the W-M sheet galaxies do not show hints
of gravitational influence from the Virgo cluster. The filamentary structures
identified can now be used to better understand the generic role of filaments
in the build-up of galaxy clusters at z~$\approx$~0.
