Finding the most influential player(s) in a social network is a very broad question and there are many ways to approach this which depend on your data and the problem you are attempting to answer/model. In particular, the relationships (edges) in the network should imply influence between players (nodes). Assuming the relationships (edges) and players (nodes) are uniform for the network, you can begin to identify players with influence in the network by using the basic nodal metrics: Degree, Betweenness, Closeness, and possibley Eigenvector Centrality, (no doubt there are more metrics and complex approaches but this is a way to get started to understand how each individual node can affect the entire network). Once multiple metrics are defined for all the nodes in the network, you can begin to identify those nodes which rank highly in multiple metrics.
Again, this is a simplistic approach to understanding each player (node), and there are many more approaches of greater complexity.