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===Game-theoretic centrality===

===Game-theoretic centrality===

The common feature of most of the aforementioned standard measures is that they assess the

The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur

The common feature of most of the aforementioned standard measures is that they assess the

The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur

上述大多数标准措施的共同特点是，它们通过只关注一个节点本身所扮演的角色来评估确定节点的重要性。然而, 在许多应用中，这种方法是不充分的，因为可能会发生协同作用

 

importance of a node by focusing only on the role that a node plays by itself. However,

 

 

 

 

 

在许多应用中，这种方法是不充分的，因为可能会发生协同作用

if the functioning of nodes is considered in groups.

if the functioning of nodes is considered in groups.

如果将节点的功能分组考虑。

如果将节点的功能分组考虑。

[[File:Game-theoretic centrality.png|Example of game-theoretic centrality]]

[[File:Game-theoretic centrality.png|Example of game-theoretic centrality]]

Example of game-theoretic centrality

Example of game-theoretic centrality

 

For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in  uses the Shapley value. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.

For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in  uses the Shapley value. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.

例如，考虑阻止流行病的问题。看看上面的网络图像，我们应该给哪些节点接种疫苗？基于前面描述的措施，我们希望识别在疾病传播中最重要的节点。仅仅基于中心的方法，即关注节点的个别特性，可能不是一个好主意。红色方块中的节点，单独不能阻止疾病的传播，但把它们作为一个群体来考虑，我们清楚地看到，如果疾病在节点 < math > v _ 1 </math > 、 < math > v _ 4 </math > 和 < math > v _ 5 </math > 中开始，它们就能阻止疾病的传播。博弈论中心性试图利用博弈论中的工具来研究所描述的问题和机会。本文提出的方法使用了 Shapley 值。由于 Shapley 值计算的时间复杂性，这一领域的大部分工作都集中在实现新的算法和方法，这些算法和方法依赖于网络的特殊拓扑结构或问题的特殊性质。这种方法可以将时间复杂度从指数降低到多项式。

例如，考虑阻止流行病的问题。看看上面的网络图像，我们应该给哪些节点接种疫苗？基于前面描述的措施，我们希望识别在疾病传播中最重要的节点。仅仅基于中心的方法，即关注节点的个别特性，可能不是一个好主意。红色方块中的节点，单独不能阻止疾病的传播，但把它们作为一个群体来考虑，我们清楚地看到，如果疾病在节点 < math > v _ 1 </math > 、 < math > v _ 4 </math > 和 < math > v _ 5 </math > 中开始，它们就能阻止疾病的传播。'''<font color="#ff8000"> 博弈论中心性Game-theoretic centrality</font>'''试图利用博弈论中的工具来研究所描述的问题和机会。本文提出的方法使用了 Shapley 值。由于 Shapley 值计算的时间复杂性，这一领域的大部分工作都集中在实现新的算法和方法，这些算法和方法依赖于网络的特殊拓扑结构或问题的特殊性质。这种方法可以将时间复杂度从指数级降低到多项式级。

Similarly, the solution concept authority distribution () applies the Shapley-Shubik power index, rather than the Shapley value, to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020), such as ranking U.S. colleges.

Similarly, the solution concept authority distribution () applies the Shapley-Shubik power index, rather than the Shapley value, to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020), such as ranking U.S. colleges.

同样，解概念权威分布()采用 Shapley-Shubik 幂指数，而不是 Shapley 值来衡量双方之间的直接影响。分布确实是一种产生向量中心性的类型。它用于对 Hu (2020)中的大数据对象进行排序，比如美国大学排名。

同样，'''<font color="#CD32CD"> 加权分布概念的解()The solution concept authority distribution () </font>'''采用 Shapley-Shubik 幂指数，而不是 Shapley 值来衡量双方之间的直接影响。这种分布确实是一种产生'''<font color="#ff8000"> 特征向量中心性Engenvector centrality</font>'''的类型。它用于对 Hu (2020)中的大数据对象进行排序，比如美国大学排名。

== Important limitations ==

== Important limitations ==