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.