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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. "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.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”可以被设想为与网络中的某种流动或传输有关。这使得我们可以根据重要流动或传输的类型，对中心性予以分类。这些方法将中心性划分于完全不同的类别中，也就是说适用于一种类别中的中心性往往无法适用于其他类别。<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/>

 

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 ([[Centrality#Degree centrality|degree centrality]]) to infinite walks ([[Centrality#Eigenvector centrality|eigenvalue centrality]]).<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref> 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 ([[Centrality#Degree centrality|degree centrality]]) to infinite walks ([[Centrality#Eigenvector centrality|eigenvalue centrality]]).<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref> 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.

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'''<font color="#ff8000"> 内聚性Cohesiveness</font>'''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。从一个给定顶点开始对步数计数，不同之处只在于行走的定义和计数方式。对该组描述的约束限制，从位置中心（'''<font color="#ff8000"> 度中心度Degree centrality</font>'''）到单元域（'''<font color="#ff8000"> 特征中心度Eigenvalue centrality</font>'''），观察到许多中心性都有这种相似关系，这也许可以解释这些指数之间的高阶相关性。

当根据内聚力方法对中心性进行分类时，很明显大多数中心性都将被划分于同一类别。起始于给定顶点的步数总和仅取决于步数的定义以及计数方式。这种分类方式的不足表现为它仅能较弱的描绘中心性特征，即按照一步步度（'''<font color="#ff8000"> 度中心性 degree centrality</font>'''）到无穷步步长（'''<font color="#ff8000"> 特征向量中心性 eigenvalue centrality</font>'''）的方式将中心性置于一种光谱状的分类中。对于采用类似方式定义的各种中心性的观察也表明了这些指数之间的高阶相关性。

===Characterization by network flows==

===Characterization by network flows==