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==Degree centrality==

==Degree centrality==

 

{{Main|Degree (graph theory)}}  

{{Main|Degree (graph theory)}}  

Examples of A) [[Betweenness centrality, B) Closeness centrality, C) Eigenvector centrality, D) Degree centrality, E) Harmonic centrality and F) Katz centrality of the same graph.]]

Examples of A) [[Betweenness centrality, B) Closeness centrality, C) Eigenvector centrality, D) Degree centrality, E) Harmonic centrality and F) Katz centrality of the same graph.]]

实例 a)[同一图的中心性，b)中心性，c)特征向量中心性，d)度中心性，e)调和中心性，f) Katz 中心性]

实例 '''<font color="#ff8000"> a)[中介中心性A) [[Betweenness centrality,b)紧密中心性，B) Closeness centrality, c)特征向量中心性，C) Eigenvector centrality, d)度中心性，D) Degree centrality, e)调和中心性，E) Harmonic centrality andf) 卡兹Katz 中心性]F) Katz centrality .]]</font>'''

Historically first and conceptually simplest is degree centrality, which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely indegree and outdegree. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.

Historically first and conceptually simplest is degree centrality, which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely indegree and outdegree. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.

历史上最简单的概念是度中心性，它定义为一个节点上发生的链接数量(即一个节点拥有的关系数量)。度可以根据节点捕获流经网络的任何东西(例如病毒或某些信息)的直接风险来解释。在有向网络的情况下(其中联系有方向) ，我们通常定义两个独立的度量度量度量度量度量，即 indegree 和 outdegree。因此，indegree 是指向该节点的关系数，outdegree 是指该节点指向其他节点的关系数。当关系与一些积极的方面如友谊或合作有关时，不受欢迎通常被解释为流行的一种形式，而超过程度则被解释为合群。

历史上最简单的概念是'''<font color="#ff8000"> 度中心性Degree centrality</font>'''，它定义为一个节点上发生的链接数量(即一个节点拥有的关系数量)。度可以根据节点捕获流经网络的任何东西(例如病毒或某些信息)的直接风险来解释。在有向网络的情况下(其中联系有方向) ，我们通常定义两个独立的度量，即 '''<font color="#ff8000"> 入度Indegree</font>'''和'''<font color="#ff8000"> 出度 Outdegree</font>'''。因此，'''<font color="#ff8000"> 入度indegree</font>'''是指向该节点的关系数，'''<font color="#ff8000"> 出度outdegree</font>'''是指该节点指向其他节点的关系数。当关系与一些积极的方面如友谊或合作有关时， '''<font color="#ff8000"> 入度Indegree</font>'''通常被解释为一种形式的受欢迎，而 '''<font color="#ff8000"> 出度Indegree</font>'''则被解释为合群。

Calculating degree centrality for all the nodes in a graph takes <math>\Theta(V^2)</math> in a dense adjacency matrix representation of the graph, and for edges takes <math>\Theta(E)</math> in a sparse matrix representation.

Calculating degree centrality for all the nodes in a graph takes <math>\Theta(V^2)</math> in a dense adjacency matrix representation of the graph, and for edges takes <math>\Theta(E)</math> in a sparse matrix representation.

计算一个图中所有节点的度向心性需要在图的稠密邻接矩阵表示中使用 Theta (v ^ 2) </math > ，而在稀疏矩阵表示中使用 Theta (e) </math > 。

计算一个图中所有节点的'''<font color="#ff8000"> 度中心性Degree centrality</font>'''需要在图的稠密'''<font color="#ff8000"> 邻接矩阵Adjacency matrix </font>'''表示中使用 Theta (v ^ 2) </math > ，而在稀疏矩阵表示中使用 Theta (e) </math > 。

The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of graph centralization. Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):

The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of graph centralization. Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):

节点级中心性的定义可以扩展到整个图，在这种情况下，我们说的是图的集中性。设 < math > v </math > 为 < math > g </math > 中度中心性最高的节点。让 < math > x: = (y，z) </math > 是 < math > | y | </math > 节点连接图，最大化下列数量(< math > y * </math > 是 < math > 中度最高的节点) :

节点级中心性的定义可以扩展到整个图，在这种情况下，我们指的是图的集中性。设 < math > v </math > 为 < math > g </math > 中'''<font color="#ff8000"> 度中心性Degree centrality</font>'''最高的节点。让 < math > x: = (y，z) </math > 是 < math > | y | </math > 节点连接图，最大化下列数量(< math > y * </math > 是 < math > 中度最高的节点) :

Correspondingly, the degree centralization of the graph <math>G</math> is as follows:

Correspondingly, the degree centralization of the graph <math>G</math> is as follows:

相应地，图形 < math > g </math > 的度集中性如下:

相应地，图形 < math > g </math > 的'''<font color="#ff8000"> 度中心性Degree centrality</font>'''如下:

<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math>

<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math>

< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ | v | ^ 2-3 | v | + 2} </math >  

< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ | v | ^ 2-3 | v | + 2} </math >

 

 

==Closeness centrality==

==Closeness centrality==