We propose an allocation rule that takes into account the importance of both players and their links and characterize it for a fixed network. Our characterization is along the lines of the characterization of the Position value for Network games by van den Nouweland and Slikker (2012). The allocation rule so defined admits multilateral interactions among the players through their links which distinguishes it from the other existing rules. Next, we extend our allocation rule to flexible networks à la Jackson (2005). 
A solution concept for network games: The role of multilateral interactions