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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 ofnodes with common neighbours are shown grouped into modules. An edge connectedto the module then implies a connection to each member of the module. Thus, theentire graph may be represented with much less clutter and without loss ofdetail. A recent experimental study has shown that such lossless compression ofdense graphs makes it easier to follow paths. However, computing optimal powergraphs is difficult. In this paper, we show that computing the optimalpower-graph with only one module is NP-hard and therefore likely NP-hard in thegeneral case. We give an ILP model for power graph computation and discuss whyILP and CP techniques are poorly suited to the problem. Instead, we are able tofind optimal solutions much more quickly using a custom search method. We alsoshow how to restrict this type of search to allow only limited back-tracking toprovide a heuristic that has better speed and better results than previouslyknown heuristics.

Improved Optimal and Approximate Power Graph Compression for Clearer Visualisation of Dense Graphs