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→点度中心性
===点度中心性===
===点度中心性===
历史上第一个概念上简单的中心性定义是点度中心性，定义为与节点直接相连的连边（例如，一个节点有的边的数目）。度可以理解为节点接触到在任何在网络中传播的事物（比如病毒或者信息）的可能性。在有向图中（连边具有方向性），我们经常定义两种不同的度中心测量：指向和指出。相应的，指向的定义为方向指向节点的连边数，指出的定义为节点指出方向的连边数。
当连边与友谊或者合作相关时，指向的度中心常被解释为赶潮流，指出被解释为爱交际。
对于有<math>|V|</math>个节点<math>|E|</math>条边的图<math>G:=(V,E)</math>，节点<math>v</math>的度中心定义为，
:<math>C_D(v)= \deg(v)</math>
Calculating degree centrality for all the nodes in a graph takes [[big theta|<math>\Theta(V^2)</math>]] in a [[dense matrix|dense]] [[adjacency matrix]] representation of the graph, and for edges takes <math>\Theta(E)</math> in a [[sparse matrix]] representation.
The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of ''graph centralization''.<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref> 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>):
:<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math>
Correspondingly, the degree centralization of the graph <math>G</math> is as follows:
:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math>
The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a [[star graph]]), and in this case
:<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math>
So, for any graph <math>G:=(V,E),</math>
:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math>
===接近中心性/亲密中心性===
===接近中心性/亲密中心性===