  We explore fundamental properties of the distribution of low mass dark matter
halos within the cosmic web using warm dark matter (WDM) and cold dark matter
(CDM) cosmological simulations. Using self abundance-matched mock galaxy
catalogs, we show that the distribution of dwarf galaxies in a WDM universe,
wherein low mass halo formation is heavily suppressed, is nearly
indistinguishable to that of a CDM universe whose low mass halos are not seen
because galaxy formation is suppressed below some threshold halo mass. However,
if the scatter between dwarf galaxy luminosity and halo properties is large
enough, low mass CDM halos would sometimes host relatively bright galaxies
thereby populating CDM voids with the occasional isolated galaxy and reducing
the numbers of completely empty voids. Otherwise, without high mass to light
scatter, all mock galaxy clustering statistics that we consider--the
auto-correlation function, the numbers and radial profiles of satellites, the
numbers of isolated galaxies, and the PDF of small voids--are nearly identical
in CDM and WDM. WDM voids are neither larger nor emptier than CDM voids, when
constructed from abundance-matched halo catalogs. It is thus a challenge to
determine whether the CDM problem of the over-abundance of small halos with
respect to the number density of observed dwarf galaxies has a cosmological
solution or an astrophysical solution. However, some clues about the dark
matter particle and the scatter between the properties of dwarf galaxies and
their dark matter halo hosts might be found in the cosmic web of galaxies in
future surveys of the local volume.
