更改

Lancichinetti–Fortunato–Radicchi benchmark is an algorithm that generates benchmark networks (artificial networks that resemble real-world networks). They have a priori known communities and are used to compare different community detection methods.  The advantage of the benchmark over other methods is that it accounts for the heterogeneity in the distributions of node degrees and of community sizes.

Lancichinetti–Fortunato–Radicchi benchmark is an algorithm that generates benchmark networks (artificial networks that resemble real-world networks). They have a priori known communities and are used to compare different community detection methods.  The advantage of the benchmark over other methods is that it accounts for the heterogeneity in the distributions of node degrees and of community sizes.

'''<font color="#ff8000">兰奇基内蒂-福图纳托-拉迪奇基准程序</font>'''是一种生成基准网络(类似于真实世界网络的人工网络)的算法。他们有一个预先已知的社区，用于比较不同的社区检测方法。与其他方法相比，基准测试的优点在于它解释了'''<font color="#ff8000">节点度</font>'''分布和社区规模分布的'''<font color="#ff8000">异质性</font>'''。

'''<font color="#ff8000">兰奇基内蒂-福图纳托-拉迪奇基准程序(Lancichinetti–Fortunato–Radicchi benchmark)</font>'''是一种生成基准网络(类似于真实世界网络的人工网络)的算法。他们有一个预先已知的社区，用于比较不同的社区检测方法。与其他方法相比，基准测试的优点在于它解释了'''<font color="#ff8000">节点度(node degree)''分布和社区规模分布的'''<font color="#ff8000">异质性(heterogeneity)</font>'''。

The node degrees and the community sizes are distributed according to a power law, with different exponents. The benchmark assumes that both the degree and the community size have power law distributions with different exponents, <math>\gamma</math> and <math>\beta</math>, respectively. <math>N</math> is the number of nodes and the average degree is <math>\langle k \rangle</math>. There is a mixing parameter <math>\mu</math>, which is the average fraction of neighboring nodes of a node that do not belong to any community that the benchmark node belongs to.  This parameter controls the fraction of edges that are between communities.

The node degrees and the community sizes are distributed according to a power law, with different exponents. The benchmark assumes that both the degree and the community size have power law distributions with different exponents, <math>\gamma</math> and <math>\beta</math>, respectively. <math>N</math> is the number of nodes and the average degree is <math>\langle k \rangle</math>. There is a mixing parameter <math>\mu</math>, which is the average fraction of neighboring nodes of a node that do not belong to any community that the benchmark node belongs to.  This parameter controls the fraction of edges that are between communities.

节点度和社区规模按幂律分布，但指数不同。基准测试假设度和社区规模都具有不同指数的'''<font color="#ff8000">幂律分布</font>'''，分别为'''<font color="#32CD32">此处需插入公式</font>'''和'''<font color="#32CD32">此处需插入公式</font>'''。'''<font color="#32CD32">此处需插入公式</font>'''是节点的数量，平均度为'''<font color="#32CD32">此处需插入公式</font>'''。混合参数'''<font color="#32CD32">此处需插入公式</font>'''是一个节点的相邻节点的平均比例，这些相邻节点不属于基准节点所属的任何社区。这个参数控制着社区之间的边缘比例。

节点度和社区规模按幂律分布，但指数不同。基准测试假设度和社区规模都具有不同指数的'''<font color="#ff8000">幂律(power law)</font>'''分布，分别为'''<font color="#32CD32">此处需插入公式</font>'''和'''<font color="#32CD32">此处需插入公式</font>'''。'''<font color="#32CD32">此处需插入公式</font>'''是节点的数量，平均度为'''<font color="#32CD32">此处需插入公式</font>'''。混合参数'''<font color="#32CD32">此处需插入公式</font>'''是一个节点的相邻节点的平均比例，这些相邻节点不属于基准节点所属的任何社区。这个参数控制着社区之间的边缘比例。