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→Closeness centrality
==Closeness centrality==
==Closeness centrality==
=='''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''==
{{Main|Closeness centrality}}In a [[Connected component (graph theory)|connected]] [[Graph (discrete mathematics)|graph]], the [[Normalization (statistics)|normalized]] '''closeness centrality''' (or '''closeness''') of a node is the average length of the [[Shortest path problem|shortest path]] between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.
{{Main|Closeness centrality}}In a [[Connected component (graph theory)|connected]] [[Graph (discrete mathematics)|graph]], the [[Normalization (statistics)|normalized]] '''closeness centrality''' (or '''closeness''') of a node is the average length of the [[Shortest path problem|shortest path]] between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.
In a connected graph, the normalized closeness centrality (or closeness) of a node is the average length of the shortest path between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.
In a connected graph, the normalized closeness centrality (or closeness) of a node is the average length of the shortest path between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.
在连通图中，节点的标准'''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''(或贴近性)是节点与图中所有其他节点之间最短路径的平均长度。因此，一个节点越是中心，它就越接近所有其他节点。
where <math>d(y,x)</math> is the distance between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.
where <math>d(y,x)</math> is the distance between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.
其中 < math > d (y，x) </math > 是顶点 < math > x </math > 和 < math > y </math > 之间的距离。然而，当谈到亲密中心性时，人们通常会提到它的规范化形式，一般是以前的公式乘以 < math > N-1 </math > ，其中 < math > n </math > 是图中的节点数。这种调整允许比较不同大小图形的节点。
其中 < math > d (y，x) </math > 是顶点 < math > x </math > 和 < math > y </math > 之间的距离。然而，当谈到'''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''时，人们通常会提到它的标准化形式，一般是以前的公式乘以 < math > N-1 </math > ，其中 < math > n </math > 是图中的节点数。这种调整允许比较不同大小图形的节点。
Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).
Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).
从所有其他节点或到所有其他节点的距离在'''<font color="#ff8000"> 无向图Undirected graphs</font>'''中是不相关的，但是在'''<font color="#ff8000"> 有向图Directed graphs</font>'''中可能产生完全不同的结果(例如:一个网站可以从传出链接获得高的'''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''，而从传入链接获得低的'''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''）。
===Harmonic centrality===
===Harmonic centrality===
=='''<font color="#ff8000"> 调和中心性Harmonic centrality</font>'''==
In a (not necessarily connected) graph, the '''harmonic centrality''' reverses the sum and reciprocal operations in the definition of closeness centrality:
In a (not necessarily connected) graph, the '''harmonic centrality''' reverses the sum and reciprocal operations in the definition of closeness centrality:
In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:
In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:
在一个(不一定是连通的)图中，调和中心性反转了封闭中心性定义中的和互反运算:
在一个(不一定是连通的)图中，'''<font color="#ff8000"> 调和中心性Harmonic centrality</font>'''反转了'''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''定义中的和互反运算:
调和中心性是由 Marchiori 和 Latora (2000)提出的，然后是 Dekker (2005)独立提出的，使用的名称是“有价值的中心性” ，Rochat (2009)。
调和中心性是由 Marchiori 和 Latora (2000)提出的，然后是 Dekker (2005)独立提出的，使用的名称是“有价值的中心性” ，Rochat (2009)。
==Betweenness centrality==
==Betweenness centrality==