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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是以图顶点上的实值函数为基础给出的，在这些顶点上产生的值被期望提供一个排名来识别最重要的节点。< 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 |  

 

< 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.

"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.

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态度来分类时，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行走次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。

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.

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 ==