A new class of geometric statistics for analyzing galaxy catalogs is presented . 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 et al . ( 1996 ) , the CfA1-like mock redshift catalogs of Nolthenius , Klypin and Primack ( 1994 , 1996 ) , and the CfA1 catalog .
We also apply the moment-based shape statistics developed by Babul & Starkman ( 1992 ) , Luo & Vishniac ( 1995 ) , and Robinson & Albrecht ( 1996 ) to these same catalogs , and compare their robustness and discriminatory power versus filament statistics .
For 100 Mpc periodic simulation boxes ( H _ { 0 } = 50 km s ^ { -1 } Mpc ^ { -1 } ) , we find discrimination of \sim 4 \sigma ( where \sigma represents resampling errors ) between CHDM and CDM for selected filament statistics and shape statistics , including variations in the galaxy identification scheme .
Comparing the CfA1 data versus the models does not yield a conclusively favored model ; no model is excluded at more than a \sim 2 \sigma level for any statistic , not including cosmic variance which could further degrade the discriminatory power .
We find that CfA1 discriminates between models poorly mainly due to its sparseness and small number of galaxies , not due to redshift distortion , magnitude limiting , or geometrical effects .
We anticipate that the proliferation of large redshift surveys and simulations will enable the statistics presented here to provide robust discrimination between large-scale structure in various cosmological models .