A generalized Pólya's urn with graph based interactions

Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability proportional to its current number of balls raised by some fixed power α>0 . We characterize the limiting behavior of the proportion of balls in the bins.

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