Recently, a new mathematical formulation of evolutionary game dynamics has been introduced accounting for a finite number of players organized over a network, where the players are located at the nodes of a graph and edges represent connections between them. Internal steady states are particularly interesting in control and consensus problems, especially in a networked context where they are related to the coexistence of different strategies. In this paper we consider this model including self loops. Existence of internal steady states is studied for different kind of graph topologies. Results on the effect of removing links from central players are also presented.