FocusCores of Multilayer Graphs

Mining dense subgraphs on multilayer graphs offers the opportunity for more in-depth discoveries than classical dense subgraph mining on single-layer graphs. However, the existing approaches fail to ensure the denseness of a discovered subgraph on layers of users’ interest and simultaneously gain partial supports on the denseness from other layers. In this paper, we introduce a novel dense subgraph model called <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Fo</u>cus<underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Core</u> (FoCore for short) for multilayer graphs, which can pay more attention to the layers focused by users. The FoCore decomposition problem, that is, identifying all nonempty FoCores in a multilayer graph, can be addressed by executing the peeling process with respect to all possible configurations of focus and background layers. Using the nice properties of FoCores, we devise an interleaved peeling algorithm and a vertex-centric algorithm toward efficient FoCore decomposition. We further design a novel cache to minimize the average retrieval time for an arbitrary FoCore without the need for full FoCore decomposition, which significantly improves efficiency in large-scale graph mining tasks. As an application, we propose a FoCore-decomposition-based algorithm to approximate the densest subgraph in a multilayer graph with a provable approximation guarantee. The extensive experiments on real-world datasets verify the effectiveness of the FoCore model and the efficiency of the proposed algorithms.