In mathematics, the term "graded" has a number of meanings, mostly related: In abstract algebra, it refers to a family of concepts: An algebraic structure X {\displaystyle X} is said to be I {\displaystyle I} -graded for an index set I {\displaystyle I} if it has a gradation or grading, i.e. a decomposition into a direct sum X = ⨁ i ∈ I X i {\textstyle X=\bigoplus _{i\in I}X_{i}} of structures; the elements of X i {\displaystyle X_{i}} are said to be "homogeneous of degree i ". Wikipedia