This paper proposes a mathematical model of network formation with general method of share of the link costs. In some published papers of the network formation, it is assumed that all players pay the same amount of cost for forming or maintaining a link, or a player who offers to form a new link pays all of the link cost. In this paper, a mathematical model of network formation with general allocation procedures of the link cost is constructed, and examine stability of the networks. It is assumed that each link cost is shared by a pair of players connected by the link unequally with a fixed fraction. In this paper, it is indicated that the network with certain structure such as the empty, the complete and a star can be stable.