Finding Connected Subgraphs of Fixed Minimum Density: Implementation and Experiments

We consider the following problem. Given a graph and a rational number μ, 0 < μ ≤ 1, find a connected subgraph of density at least μ with the largest number of vertices. Here, the density of an nvertex graph with m edges is m/ ( n 2 ) . This problem arises in many application contexts such as community detection in social networks. We implement a branch and bound algorithm and tune it for efficiency on sparse real-world graphs for the case μ ≥ 1/2. Central issues for the implementation are the choice of branching candidates, two new upper bounding procedures, and several data reduction and early termination rules.