HI Sahab,
Eigenvector centrality is used to measure the number of connections of the neiborhing nodes of the nodes you are getting the measure. In a directed graph, I think you can try to use a measure of eigenvector centrality that takes into account the in degree and out degree of the nodes to take into account for the direction of the interactions.
Maybe you could use closeness centrality that will show the node where that is closer to most of other nodes in terms of the interactions they share. Check out.
Best,
Hernani