  We explored the statistics of filtering of simple patterns on a number of
deterministic and random graphs as a tractable simple example of information
processing in complex systems. In this problem, multiple inputs map to the same
output, and the statistics of filtering is represented by the distribution of
this degeneracy. For a few simple filter patterns on a ring we obtained an
exact solution of the problem and described numerically more difficult filter
setups. For each of the filter patterns and networks we found a few numbers
essentially describing the statistics of filtering and compared them for
different networks. Our results for networks with diverse architectures appear
to be essentially determined by two factors: whether the graphs structure is
deterministic or random, and the vertex degree. We find that filtering in
random graphs produces a much richer statistics than in deterministic graphs.
This statistical richness is reduced by increasing the graph's degree.
