  The eccentricity matrix $\epsilon(G)$, of a connected graph $G$ is obtained
by retaining the maximum distance from each row and column of the distance
matrix of $G$ and the other entries are assigned with 0. In this paper, we
discuss the eccentricity spectrum of subdivision vertex (edge) join of regular
graphs. Also, we obtain new families of graphs having irreducible or reducible
eccentricity matrix. Furthermore, we use these results to construct infinitely
many $\epsilon-$cospectral graph pairs as well as infinitely many pairs and
triplets of $\epsilon-$cospectral $\epsilon-$equienergetic graphs. Moreover, we
present some new family of $\epsilon-$integral graphs.
