  The eccentricity matrix $\varepsilon(G)$ of a graph $G$ is obtained from the
distance matrix of $G$ by retaining the largest distances in each row and each
column, and leaving zeros in the remaining ones. The eccentricity energy of $G$
is sum of the absolute values of the eigenvalues of $\varepsilon(G)$. Although
the eccentricity matrices of graphs are closely related to the distance
matrices of graphs, a number of properties of eccentricity matrices are
substantially different from those of the distance matrices. The change in
eccentricity energy of a graph due to an edge deletion is one such property. In
this article, we give examples of graphs for which the eccentricity energy
increase (resp., decrease) but the distance energy decrease (resp., increase)
due to an edge deletion. Also, we prove that the eccentricity energy of the
complete $k$-partite graph $K_{n_1,\hdots,n_k}$ with $k\geq 2$ and $ n_i\geq
2$, increases due to an edge deletion.
