  We investigated the stability and mechanical and electronic properties of
fifteen metastable mixed $sp^2$-$sp^3$ carbon allotropes in the family of
interpenetrating graphene networks (IGNs) using density functional theory (DFT)
within the generalized gradient approximation (GGA). IGN allotropes exhibit
non-monotonic bulk and linear compressibilities before their structures
irreversibly transform into new configurations under large hydrostatic
compression. The maximum bulk compressibilities vary widely between structures
and range from 3.6 to 306 TPa$^{-1}$. We find all the IGN allotropes have
negative linear compressibilities with maximum values varying from -0.74 to
-133 TPa$^{-1}$. The maximal negative linear compressibility of Z33 (-133
TPa$^{-1}$ at 3.4 GPa) exceeds previously reported values at pressures higher
than 1.0 GPa. IGN allotropes can be classified as either armchair- or
zigzag-type, and these two types of IGNs exhibit different electronic
properties. Zigzag-type IGNs are node-line semimetals, while armchair-type IGNs
are either semiconductors or node-loop or node-line semimetals. Experimental
synthesis of these IGN allotropes might be realized since their formation
enthalpies relative to graphite are only 0.1 - 0.5 eV/atom (that of C$_{60}$
fullerene is about 0.4 eV/atom), and energetically feasible binary compound
pathways are possible.
