  A new class of geometric statistics for analyzing galaxy catalogs is
presented. {\it Filament statistics} quantify filamentarity and planarity in
large scale structure in a manner consistent with catalog visualizations. These
statistics are based on sequences of spatial links which follow local
high-density structures. From these link sequences we compute the discrete
curvature, planarity, and torsion. Filament statistics are applied to CDM and
CHDM ($\Omega_\nu = 0.3$) simulations of Klypin \etal (1995), the CfA1-like sky
catalogs of Nolthenius, Klypin and Primack (1994, 1995), and the CfA1 catalog.
For 100 Mpc periodic simulation boxes ($H_0 = 50$ km s$^{-1}$ Mpc$^{-1}$), we
find robust discrimination of over 4$\sigma$ (where $\sigma$ represents
resampling errors) between CHDM and CDM. The {\it reduced filament statistics}
show that CfA1 data is intermediate between CHDM and CDM, but more consistent
with the CHDM models. Filament statistics provide robust and discriminatory
shape statistics with which to test cosmological simulations of various models
against present and future redshift survey data.
