Although coherent large-scale structures such as filaments and walls are
apparent to the eye in galaxy redshift surveys, they have so far proven
difficult to characterize with computer algorithms. This paper presents a
procedure that uses the eigenvalues and eigenvectors of the Hessian matrix of
the galaxy density field to characterize the morphology of large-scale
structure. By analysing the smoothed density field and its Hessian matrix, we
can determine the types of structure - walls, filaments, or clumps - that
dominate the large-scale distribution of galaxies as a function of scale. We
have run the algorithm on mock galaxy distributions in a LCDM cosmological
N-body simulation and the observed galaxy distributions in the Sloan Digital
Sky Survey. The morphology of structure is similar between the two catalogues,
both being filament-dominated on 10-20 h^{-1} Mpc smoothing scales and
clump-dominated on 5 h^{-1} Mpc scales. There is evidence for walls in both
distributions, but walls are not the dominant structures on scales smaller than
~25 h^{-1} Mpc. Analysis of the simulation suggests that, on a given comoving
smoothing scale, structures evolve with time from walls to filaments to clumps,
where those found on smaller smoothing scales are further in this progression
at a given time.Comment: 37 pages, 14 figures. Accepted to MNRAS
