  Nodes in real-world networks are repeatedly observed to form dense clusters,
often referred to as communities. Methods to detect these groups of nodes
usually maximize an objective function, which implicitly contains the
definition of a community. We here analyze a recently proposed measure called
surprise, which assesses the quality of the partition of a network into
communities. In its current form, the formulation of surprise is rather
difficult to analyze. We here therefore develop an accurate asymptotic
approximation. This allows for the development of an efficient algorithm for
optimizing surprise. Incidentally, this leads to a straightforward extension of
surprise to weighted graphs. Additionally, the approximation makes it possible
to analyze surprise more closely and compare it to other methods, especially
modularity. We show that surprise is (nearly) unaffected by the well known
resolution limit, a particular problem for modularity. However, surprise may
tend to overestimate the number of communities, whereas they may be
underestimated by modularity. In short, surprise works well in the limit of
many small communities, whereas modularity works better in the limit of few
large communities. In this sense, surprise is more discriminative than
modularity, and may find communities where modularity fails to discern any
structure.
