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Formulas for vertex eccentricity and radius for the n-fold tensor product $G={\otimes }_{i=1}ⁿG_i$ of n arbitrary simple graphs $G_i$ are derived. The center of G is characterized as the union of n+1 vertex sets of form V₁×V₂×...×Vₙ, with $V_i\subseteq V\left(G_i\right)$.