<p>We introduce a class of player-based allocation rules for Network Games, which we refer as the Network Egalitarian-Myerson values. Each member of this class is obtained by a convex combination of the Network Myerson value, and the Component-wise Equal Division rule determined by a convexity parameter. In Network Games under the cooperative framework, the Network Myerson value is an extreme example of marginalism, while the Component-wise Equal Division rule signifies egalitarianism. The convexity parameter in the proposed value combines these two attributes and determines the degree of solidarity to the players. Here, by solidarity, we mean the mutual support or compensation among the players in a network. We present two characterizations of the Network Egalitarian-Myerson value. Further, we propose an implementation mechanism for the proposed class under sub-game perfect Nash equilibrium.</p>