A type of evolution of graphs with maximum vertex degree at most d is introduced. This evolution can start from any initial graph whose set of vertices of degree less than d is independent. The main concern is the regularity of graphs generated by this graph process when the initial graph has no edges. By analysis of the solutions of systems of differential equations it is shown that the final graph of this evolution is asymptotically almost surely a d-regular graph (subject to the usual parity condition).