  Drawings of highly connected (dense) graphs can be very difficult to read.
Power Graph Analysis offers an alternate way to draw a graph in which sets of
nodes with common neighbours are shown grouped into modules. An edge connected
to the module then implies a connection to each member of the module. Thus, the
entire graph may be represented with much less clutter and without loss of
detail. A recent experimental study has shown that such lossless compression of
dense graphs makes it easier to follow paths. However, computing optimal power
graphs is difficult. In this paper, we show that computing the optimal
power-graph with only one module is NP-hard and therefore likely NP-hard in the
general case. We give an ILP model for power graph computation and discuss why
ILP and CP techniques are poorly suited to the problem. Instead, we are able to
find optimal solutions much more quickly using a custom search method. We also
show how to restrict this type of search to allow only limited back-tracking to
provide a heuristic that has better speed and better results than previously
known heuristics.
