  The eccentricity (anti-adjacency) matrix $\varepsilon(G)$ of a graph $G$ is
obtained from the distance matrix by retaining the eccentricities in each row
and each column. This matrix is first defined in 2018 by Wang et al. \cite{1}.
In this paper we have characterized the graphs which have at most one (hence
exactly) positive eigenvalue of $\varepsilon(G)$.
