MEGA: merger graphs of structure formation

When following the growth of structure in the Universe, we propose replacing merger trees with merger graphs, in which haloes can both merge and split into separate pieces. We show that this leads to smoother mass growth and eliminates catastrophic failures in which massive haloes have no progenitors or descendants. For those who prefer to stick with merger trees, we find that trees derived from our merger graphs have similar mass growth properties to previous methods, but again without catastrophic failures. For future galaxy formation modelling, two different density thresholds can be used to distinguish host haloes (extended galactic haloes, groups and clusters) from higher-density subhaloes: sites of galaxy formation.