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.
This can be done because a siteiwith no inputs will havexi = 1at all FPs, and if siteiis an input to sitejthen at all FPsx j = 0, so sitejdoes not affect any other site
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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.