  We present a proof of concept of a new galaxy group finder method, Markov
graph Clustering (MCL; Van Dongen 2000) that naturally handles probabilistic
linking criteria. We introduce a new figure of merit, the variation of
information statistic (VI; Meila 2003), used to optimise the free parameter(s)
of the MCL algorithm. We explain that the common Friends-of-Friends (FoF)
method is a subset of MCL. We test MCL in real space on a realistic mock galaxy
catalogue constructed from a N-body simulation using the GALFORM model. With a
fixed linking length FoF produces the best group catalogues as quantified by
the VI statistic. By making the linking length sensitive to the local galaxy
density, the quality of the FoF and MCL group catalogues improve significantly,
with MCL being preferred over FoF due to a smaller VI value. The MCL group
catalogue recovers accurately the underlying halo multiplicity function at all
multiplicities. MCL provides better and more consistent group purity and halo
completeness values at all multiplicities than FoF. As MCL allows for
probabilistic pairwise connections, it is a promising algorithm to find galaxy
groups in photometric surveys.
