# 集聚系数

## 整体集聚系数

${\displaystyle L(i)=\left\{v_{j}:e_{ij}\in E\land e_{ji}\in E\right\}}$

L(i) 里的边的数量就是顶点 ${\displaystyle v_{i}}$ 的度，记作 ${\displaystyle k_{i}}$${\displaystyle k_{i}=|L(i)|}$

${\displaystyle C_{total}(G)={\frac {3\times G_{\triangle }}{3\times G_{\triangle }+G_{\land }}}}$

${\displaystyle C_{total}(G)={\frac {3\times G_{\triangle }}{\sum _{i=1}^{n}{\binom {k_{i}}{2}}}}}$[5]

## 局部集聚系数

${\displaystyle C(i)={\frac {2{\Big |}{\Big \{}e_{jk}:v_{j},v_{k}\in L(i),e_{jk}\in E{\Big \}}{\Big |}}{k_{i}(k_{i}-1)}}.}$

${\displaystyle C(i)={\frac {{\Big |}{\Big \{}e_{jk}:v_{j},v_{k}\in L(i),e_{jk}\in E{\Big \}}{\Big |}}{k_{i}(k_{i}-1)}}.}$

${\displaystyle C(i)={\frac {\lambda _{G}(v_{i})}{\tau _{G}(v_{i})+\lambda _{G}(v_{i})}}.}$

${\displaystyle \tau _{G}(v_{i})+\lambda _{G}(v_{i})=C({k_{i}},2)={\frac {1}{2}}k_{i}(k_{i}-1).}$

## 平均集聚系数

${\displaystyle {\bar {C}}={\frac {1}{n}}\sum _{i=1}^{n}C(i).}$

${\displaystyle {\bar {C}}={\frac {1}{n}}\sum _{i=1}^{n}C(i)={\frac {1}{n}}\sum _{i=1}^{n}{\frac {\lambda _{G}(v_{i})}{\tau _{G}(v_{i})+\lambda _{G}(v_{i})}}}$
${\displaystyle C_{total}(G)={\frac {\sum _{i=1}^{n}\lambda _{G}(v_{i})}{\sum _{i=1}^{n}\left(\tau _{G}(v_{i})+\lambda _{G}(v_{i})\right)}}}$

## 参考来源

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