"Phase Transitions if Random Graphical Dynamical Systems"
Random graphical dynamical systems are systems which evolve in time to generate large scale graphical networks. Previous work has demonstrated the existence of stochastic phase transitions which possess critical parameters distinct from those that appear in standard random graphs. This is a reflection of the dynamical nature of the graph in an RGDS as opposed to the fixed nature of a random graph. A critical parameter has been shown to be the sociability, defined as the maximal number of connections which can form at a given vertex. A new RGDS model is presented in which the only tunable parameter is the sociability. A double stochastic pahse transition is illustrated, in which the probablity distribution of conencted cluster sizes first shifts from unimodal to bimodal biased towards mow clusters, and then shifts again towards bimodal baised towards large clusters.