  Hierarchical theories of structure formation predict that clusters of
galaxies should be embedded in a web like structure, with filaments emanating
from them to large distances. The amount of mass contained within such
filaments near a cluster can be comparable to the collapsed mass of the cluster
itself. Diffuse infalling material also contains a large amount of mass. Both
these components can contribute to the cluster weak lensing signal. This
``projection bias'' is maximized if a filament lies close to the line-of-sight
to a cluster. Using large--scale numerical simulations of structure formation
in a cosmological constant dominated cold dark matter model, we show that the
projected mass typically exceeds the actual mass by several tens of percent.
This effect is significant for attempts to estimate cluster masses through weak
lensing observations, and will affect weak lensing surveys aimed at
constructing the cluster mass function.
