Analyize or simulate the following model
Start with a urn containing two balls, one red and one black. At each unit of time select a ball from
the urn and then replace it along with another ball of the same color. This is equivalent to preferential
adding of balls to the urn where at each step we add a red or black ball where the color is selected
randomly with probabilities proportional to the number of red and black balls.
Consider an urn with k different types of balls. Each type of ball corresponds to a vertex of a graph.
The number of balls of a given type corresponds to the degree of the vertex. At each unit of time draw
a ball from the urn, replace it in the urn along with another ball of the same type plus a ball of a
new type k+1.