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.
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