Alternatives to Graph theory?
According to graph theory, wouldn't this make Person B also very influential?

No. You need to think about how to set up your graph first and then go further. In this case your graph is not simple but both weighted and directed thus handling a request of B by A neither reduces A's influence nor improves B's. Because the weights of directed edges are determining the influence.

Is there a better way than just counting number of interactions?

Community Detection or what computer scientists call Graph Clustering. If you do not have to limit yourself to hierarchies, you can extract communities who have the most interaction and share suggestions inside the community.