Recently, exponent matrices have emerged as a dynamic tool for studying networks by measuring node centrality. In this work, we define a Symmetric Neighbors degree sum exponent matrix $S_{N}E(G)$ of a graph $G$ whose $(i,j)^{th}$ entry is $\delta_i^{\delta_j}+\delta_j^{\delta_i}$ for $i\neq j$, it is zero otherwise, where $\delta_i$ is the Neighbors degree sum of a vertex $v_i$ in $G$. Inspired by the applications of Neighbors degree sum in redefining various degree based topological indices, we introduce characteristic polynomial of $S_{N}E(G)$, termed as Symmetric Neighbors degree sum exponent polynomial and the sum of absolute value of eigenvalue of $S_{N}E(G)$ matrix is called as Symmetric Neighbors degree sum exponent energy. In this paper, we obtain the Neighbors degree sum exponent polynomial and Neighbors degree sum exponent energy of some graphs.