  A widely-used operation on graphs is local clustering, i.e., extracting a
well-characterized community around a seed node without the need to process the
whole graph. Recently local motif clustering has been proposed: it looks for a
local cluster based on the distribution of motifs. Since this local clustering
perspective is relatively new, most approaches proposed for it are extensions
of statistical and numerical methods previously used for edge-based local
clustering, while the available combinatorial approaches are still few and
relatively simple. In this work, we build a hypergraph and a graph model which
both represent the motif-distribution around the seed node. We solve these
models using sophisticated combinatorial algorithms designed for (hyper)graph
partitioning. In extensive experiments with the triangle motif, we observe that
our algorithm computes communities with a motif conductance value being one
third on average in comparison against the communities computed by the
state-of-the-art tool MAPPR while being 6.3 times faster on average.
