In particular, let A {\displaystyle \mathbf {A} } be the graph adjacency matrix: then, one can define A ~ = A + I {\displaystyle {\tilde {\mathbf {A} }}=\mathbf {A} +\mathbf {I} } and D ~ i i = ∑ j ∈ V A ~ i j {\displaystyle {\tilde {\mathbf {D} }}_{ii}=\sum _{j\in V}{\tilde {A}}_{ij}} , where I {\displaystyle \mathbf {I} } denotes the identity matrix. This normalization ensures that the eigenvalues of D ~ − 1 2 A ~ D ~ − 1 2 {\displaystyle {\tilde {\mathbf {D} }}^{-{\frac {1}{2}}}{\tilde {\mathbf {A} }}{\tilde {\mathbf {D} }}^{-{\frac {1}{2}}}} are bounded in the range [ 0 , 1 ] {\displaystyle [0,1]} , avoiding numerical instabilities and exploding/vanishing gradients.