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是圖形的當且僅當頂點度的總和為偶數且序列服從以下性質
(Skiena 1990, p. 157)，並且此條件也推廣到有向圖。 Tripathi 和 Vijay (2003) 表明，此不等式只需要檢查序列中不同項的數量，而不需要檢查所有 
，而不是所有 
。
和 
的度序列是圖形的當且僅當序列 
是圖形的。此外，Havel (1955) 和 Hakimi (1962) 表明，如果度序列是圖形的，則存在一個圖 
，使得最高度數的節點與
個次最高度數頂點相鄰，其中 
，其中 
是 
的最大頂點度。