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→Definition and characterization of centrality indices
Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |
Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |
中心性指数是对“重要顶点的特征是什么”这一问题的回答，答案以图顶点的实值函数的方式给出，在这些顶点上的取值的排序标识出最重要的节点。
< ref name = “ Christian f. a. Negre，Uriel n. Morzan，Heidi p. Hendrickson，Rhitankar Pal，George p. Lisi，j. Patrick Loria，Ivan Rivalta，Junming Ho，Victor s. Batista。2018 E12201-- E12208” > { cite journal |
author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|
author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|
The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.
The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.
“重要性”这个词有许多含义，导致了许多不同的中心性定义。分为两类。
"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important.<ref name=Borgatti2005/> "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref> Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<ref name=Borgatti2005/>
"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important.<ref name=Borgatti2005/> "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref> Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<ref name=Borgatti2005/>
"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important. Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.
"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important. Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.
“重要性”可以被认为与一种跨网络的流动或传输有关。这允许根据它们认为重要的流类型对集中性进行分类。这两种方法都将集中性划分为不同的类别。进一步的推论是，适用于一个类别的中心性在（推广）应用于另一个类别时往往会“出错”。
When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one (degree centrality) to infinite walks (eigenvalue centrality). The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.
When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one (degree centrality) to infinite walks (eigenvalue centrality). The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.
当中心性按照它们对内聚性的趋近程度来分类时，很明显，大多数中心性都集中在一个类别中。从一个给定的顶点开始的步数的计数只在行走的定义和计数方式上有所不同。限制对这个群体的考虑允许一个软角色塑造，它将集中点放在一个从一级行走(度集中性)到无限行走(特征值集中性)的频谱上。观察到许多中心分享这种家庭关系，也许可以解释这些指数之间的高阶相关性。
A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once.<ref name=Borgatti2005/>
A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once.<ref name=Borgatti2005/>
A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once.
A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at oe.
一个网络可以被看成是对某种物体流动的路径描述。使基于流的类型和由中心性编码的路径类型（同时）得到表征。一个流可以基于传输，每个不可分割的项目从一个节点到另一个节点，就像一个包裹从配送站送到客户的房子。第二种情况是串行复制，在这种情况下，一个项从源节点被复制到达目标节点。例如通过流言传播信息，以私有方式传播信息，并在流程结束时通知源节点和目标节点。最后一种情况是并行复制，即同时将项目复制到多个链接，就像无线电广播一次性向多个听众提供相同的信息。
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，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。
== Important limitations ==
== Important limitations ==