We consider configuration graphs with N vertices. The vertex degrees are independent equally distributed random variables whose distribution satisfies the following condition: as k→∞
p_k = P{ξ = k} ∼ h(k) / k^τ+1, τ>0,
where the random value η is equal to the degree of any vertex of the graph and the function h(x) is slowly varying (in the Karamata sense). The global clustering coefficient of a conditional configuration graph is investigated for different values of the parameter τ > 0. Limit theorems are obtained for this characteristic as the number of vertices tends to infinity.