Abstract
An initially empty (no edges) graph of the order of M is assumed to evolve by adding one edge at a time. This edge can connect either two linked components and form a new component of a larger order (coalescence of graphs) or increase (by one) the number of edges in a given linked component. The evolution equation for the generating functional of the probability to find in the system a given set of occupation numbers (the numbers of graphs of the order of g having exactly ν edges) at time t is formulated and solved exactly. The expression for the graph composition spectrum is derived and analysed in the limit of large M.
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