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In this paper the time evolution of a finite bipartite graph initially comprising two sorts of isolated vertices is considered. The graph is assumed to evolve by adding edges, one at a time. Each new edge connects either two linked components and forms a new component of a larger order (coalescence of graphs) or increases (by one) the number of edges in a given linked component (cycling). Any state of the graph is thus characterized by the set of occupation numbers (the numbers of linked components comprising a given numbers of vertexes of
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