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=== 平均最短路径长度（特征路径长度） ===

=== 平均最短路径长度（特征路径长度） ===

The average shortest path length is calculated by finding the shortest path between all pairs of nodes, and taking the average over all paths of the length thereof (the length being the number of intermediate edges contained in the path, i.e., the distance <math>d_{u,v}</math> between the two vertices <math>u,v</math> within the graph). This shows us, on average, the number of steps it takes to get from one member of the network to another. The behavior of the expected average shortest path length (that is, the ensemble average of the average shortest path length) as a function of the number of vertices <math>N</math> of a random network model defines whether that model exhibits the small-world effect; if it scales as <math>O(\ln N)</math>, the model generates small-world nets. For faster-than-logarithmic growth, the model does not produce small worlds. The special case of <math>O(\ln\ln N)</math> is known as ultra-small world effect.

The average shortest path length is calculated by finding the shortest path between all pairs of nodes, and taking the average over all paths of the length thereof (the length being the number of intermediate edges contained in the path, i.e., the distance <math>d_{u,v}</math> between the two vertices <math>u,v</math> within the graph). This shows us, on average, the number of steps it takes to get from one member of the network to another. The behavior of the expected average shortest path length (that is, the ensemble average of the average shortest path length) as a function of the number of vertices <math>N</math> of a random network model defines whether that model exhibits the small-world effect; if it scales as <math>O(\ln N)</math>, the model generates small-world nets. For faster-than-logarithmic growth, the model does not produce small worlds. The special case of <math>O(\ln\ln N)</math> is known as ultra-small world effect.

平均最短路径长度的计算方法是找到所有节点对之间的最短路径，并取其长度所有路径的平均值(其长度为路径中包含的中间边的数目，即图中两个顶点之间的距离{ displaystyle d { u，v }})。 这向我们展示了从网络中的一个成员到另一个成员所需的平均步数。 期望平均最短路径长度(即平均最短路径长度的总体均值)作为一个随机网络模型的顶点数 n } n 的函数的行为定义了该模型是否表现出小世界效应; 如果它缩放为{ displaystyle o (ln n)} ，则该模型生成小世界网。 对于比对数更快的增长，该模型不会产生小世界。 超小世界效应(ultra-small world effect)是超小世界效应的特例。

平均最短路径长度的计算方法是找到所有节点对之间的最短路径，并取其长度所有路径的平均值（其长度为路径中包含的中间边的数目，即图中两个顶点 <math>u,v</math> 之间的距离<math>d_{u,v}</math>）。这向我们展示了从网络中的一个成员到另一个成员所需的平均步数。期望平均最短路径长度（即平均最短路径长度的总体均值）作为随机网络模型的顶点数 <math>N</math> 的函数的行为定义了该模型是否表现出小世界效应；如果它变为 <math>O(\ln N)</math> ，则该模型生成小世界网络。对于比对数更快的增长，该模型不会产生小世界。<math>O(\ln\ln N)</math>的特例是超小世界效应。

 

=== 网络半径 ===

=== 网络半径 ===