This paper studies the connections model (Jackson and Wolinsky, 1996) when nodes may have different values. It is shown that efficiency is reached by a strongly hierarchical structure that we call strong NSG-networks: Nested Split Graph networks where the hierarchy or ranking of nodes inherent in any such network is consistent with the rank of nodes according to their value, perhaps leaving some of the nodes with the lowest values disconnected. A simple algorithm is provided for calculating these efficient networks. We also introduce a natural extension of pairwise stability assuming that players are allowed to agree on how the cost of each link is split and prove that stability in this sense for connected strong NSG-networks entails efficiency.

本文研究了节点可能具有不同值时的连接模型（Jackson 和 Wolinsky，1996）。结果表明，通过我们称为强 NSG 网络的强层次结构来实现效率：嵌套拆分图网络，其中任何此类网络中固有的节点的层次结构或排名与根据节点值的节点排名一致，也许离开一些具有最低值的节点断开连接。提供了一种简单的算法来计算这些高效网络。我们还引入了成对稳定性的自然扩展，假设允许玩家就每个链接的成本如何分配达成一致，并证明连接的强 NSG 网络在这种意义上的稳定性需要效率。