The eccentricity matrix of a digraph

The eccentricity matrix of a digraph is obtained from the distance matrix by keeping the largest distances in each row and each column, and leaving 0 in the remaining ones. Randić (2013) first defined D_MAX-matrix of a graph and renamed it as eccentricity matrix by Wang et al. (2018). In this paper, we extend the concept of the eccentricity matrix of a graph to a digraph. We consider the irreducibility of the eccentricity matrix of a digraph with diameter 2 and obtain the lower bounds of ɛ-energy of a digraph with diameter 2. We characterize the lower bound of the spectral radius of the eccentricity matrix of a digraph and the corresponding extremal digraphs. Moreover, we give the ɛ-spectra and ɛ-energies of some digraphs.