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Many large scale complex networks exhibit a scale free vertex degree distribution in a power law form.To better understand the mechanism of power law formation in real world networks, we explore and analyze the underlying mechanism based on the vertex degree sequences of such networks.We show that for a scale free network of size N, if its vertex degree sequence is k1 < k2 < … < k1, and if its power exponent satisfies y > 1,then the length I of the vertex degree sequence is of order log N.We verify this conclusion by a co authorship network and some other real networks in various areas.