In this paper, we obtain the eccentricity spectrum and irreducibility of eccentricity matrix of the generalized friendship graph which is a generalization of the results in [12]. Also, we study the irreducibility of eccentricity matrix the H-join of graphs. As a consequence, we deduce a result in [12]. Further, we characterize graphs for which the eccentricity matrix of the generalized corona product of them is irreducible. As a result, we deduce a result in [11].