Connectivity-Based Phase Transition
Connectivity-Based Phase Transition
This Demonstration allows the connection of a graph of vertices (nodes) by edges (links) drawn in either orderly or random fashion to illustrate how the graph undergoes a transition between two states, D and C, where D is a disconnected set of individual vertices and C is a single connected cluster of all the vertices. Edges are undirected and node locations are unimportant, but they are placed at the vertices of a regular -gon to simplify the drawing. Since no additional properties are assumed, the change of state from D to C can be interpreted as an abstract phase transition based solely on connectivity. Regardless of the number of vertices and edges drawn, when the number of vertices in the largest connected cluster is plotted against the edges-to-vertices ratio, the transition occurs around an edges-to-vertices ratio of 1/2, which is shown as a dashed green vertical line on the phase transition plot.
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