The maximum number of edge-disjoint spanning trees in a network has been used as a measure of the strength of a network. It gives the number of disjoint ways that the network can be fully connected. This suggests a game theoretic analysis that shows the relative importance of the different links to form a strong network. We introduce the Network strength game as a cooperative game defined on a graph $$G=(V,E)$$ G = ( V , E ) . The player set is the edge-set E and the value of a coalition $$S \subseteq E$$ S ⊆ E is the maximum number of disjoint spanning trees included in S . We study the core of this game, and we give a polynomial combinatorial algorithm to compute the nucleolus when the core is non-empty.

中文翻译：

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网络力量游戏：核心与核仁

网络中边不相交生成树的最大数量已被用作衡量网络强度的指标。它给出了网络可以完全连接的不相交方式的数量。这表明了一种博弈论分析，该分析显示了形成强大网络的不同链接的相对重要性。我们将网络强度游戏介绍为在图 $$G=(V,E)$$ G = (V, E) 上定义的合作游戏。参与者集是边集 E 并且联盟 $$S \subseteq E$$ S ⊆ E 的值是 S 中包含的不相交生成树的最大数量。我们研究了这个游戏的核心，我们给出了一个多项式组合算法来计算核心非空时的核仁。