A Simple Heuristic for the Graph Tukey Depth Problem with Potential Applications to Graph Mining

We study a recently introduced adaptation of Tukey depth to graphs and discuss its algorithmic properties and potential applications to mining and learning with graphs. In particular, since it is NP-hard to compute the Tukey depth of a node, as a first contribution we provide a simple heuristic based on maximal closed set separation in graphs and show empirically on different graph datasets that its approximation error is small. Our second contribution is concerned with geodesic core-periphery decompositions of graphs. We show empirically that the geodesic core of a graph consists of those nodes that have a high Tukey depth. This information allows for a parameterized deterministic definition of the geodesic core of a graph.