Mining Frequent Neighborhood Patterns in Large Labeled Graphs

Over the years, frequent subgraphs have been an important sort of targeted patterns in the pattern mining literatures, where most works deal with databases holding a number of graph transactions, e.g., chemical structures of compounds. These methods rely heavily on the downward-closure property (DCP) of the support measure to ensure an efficient pruning of the candidate patterns. When switching to the emerging scenario of single-graph databases such as Google Knowledge Graph and Facebook social graph, the traditional support measure turns out to be trivial (either 0 or 1). However, to the best of our knowledge, all attempts to redefine a single-graph support resulted in measures that either lose DCP, or are no longer semantically intuitive. This paper targets mining patterns in the single-graph setting. We resolve the "DCP-intuitiveness" dilemma by shifting the mining target from frequent subgraphs to frequent neighborhoods. A neighborhood is a specific topological pattern where a vertex is embedded, and the pattern is frequent if it is shared by a large portion (above a given threshold) of vertices. We show that the new patterns not only maintain DCP, but also have equally significant semantics as subgraph patterns. Experiments on real-life datasets display the feasibility of our algorithms on relatively large graphs, as well as the capability of mining interesting knowledge that is not discovered in prior works.Comment: 9 page

Exotic orbits due to spin-spin coupling around Kerr black holes

We report exotic orbital phenomena of spinning test particles orbiting around a Kerr black hole, i.e., some orbits of spinning particles are asymmetrical about the equatorial plane. When a nonspinning test particle orbits around a Kerr black hole in a strong field region, due to relativistic orbital precessions, the pattern of trajectories is symmetrical about the equatorial plane of the Kerr black hole. However, the patterns of the spinning particles' orbit are no longer symmetrical about the equatorial plane for some orbital configurations and large spins. We argue that these asymmetrical patterns come from the spin-spin interactions between spinning particles and Kerr black holes, because the directions of spin-spin forces can be arbitrary, and distribute asymmetrically about the equatorial plane.Comment: 15 pages, 20 figure