Fixed points of Boolean networks on sparse random graphs have finite moments away from frozen-to-fluctuating transitions and organize into clusters whose number and separation change across the transition.
Sudden emergence of a giant k-core in a random graph.Journal of Combinatorial Theory, Series B, 67:111
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Fixed points of Boolean networks with sparse connections
Fixed points of Boolean networks on sparse random graphs have finite moments away from frozen-to-fluctuating transitions and organize into clusters whose number and separation change across the transition.