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We consider the random graph model G (w) for a given expected degree sequence w = (w₁, w₂, , wₙ). If the expected average degree is strictly greater than 1, then almost surely the giant component in G of G (w) has volume (i. e. , sum of weights of vertices in the giant component) equal to ₀ Vol (G) + O (n^3. 5 n), where ₀ is the unique nonzero root of the equation \ ₈=₁ⁿ wᵢ e^-wᵢ = (1-) ₈=₁ⁿ wᵢ, \ and where Vol (G) =ᵢ wᵢ.
Chung et al. (Sun,) studied this question.