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The size of a network can refer to the number of nodes <math>N</math> or, less commonly, the number of edges <math>E</math> which (for connected graphs with no multi-edges) can range from <math>N-1</math> (a tree) to <math>E_{\max}</math> (a complete graph). In the case of a simple graph (a network in which at most one (undirected) edge exists between each pair of vertices, and in which no vertices connect to themselves), we have <math>E_{\max}=\tbinom N2=N(N-1)/2</math>; for directed graphs (with no self-connected nodes), <math>E_{\max}=N(N-1)</math>; for directed graphs with self-connections allowed, <math>E_{\max}=N^2</math>. In the circumstance of a graph within which multiple edges may exist between a pair of vertices, <math>E_{\max}=\infty</math>.
The size of a network can refer to the number of nodes <math>N</math> or, less commonly, the number of edges <math>E</math> which (for connected graphs with no multi-edges) can range from <math>N-1</math> (a tree) to <math>E_{\max}</math> (a complete graph). In the case of a simple graph (a network in which at most one (undirected) edge exists between each pair of vertices, and in which no vertices connect to themselves), we have <math>E_{\max}=\tbinom N2=N(N-1)/2</math>; for directed graphs (with no self-connected nodes), <math>E_{\max}=N(N-1)</math>; for directed graphs with self-connections allowed, <math>E_{\max}=N^2</math>. In the circumstance of a graph within which multiple edges may exist between a pair of vertices, <math>E_{\max}=\infty</math>.
=== 规模 ===
=== 规模 ===
The size of a network can refer to the number of nodes <math>N</math> or, less commonly, the number of edges <math>E</math> which (for connected graphs with no multi-edges) can range from <math>N-1</math> (a tree) to <math>E_{\max}</math> (a complete graph). In the case of a simple graph (a network in which at most one (undirected) edge exists between each pair of vertices, and in which no vertices connect to themselves), we have <math>E_{\max}=\tbinom N2=N(N-1)/2</math>; for directed graphs (with no self-connected nodes), <math>E_{\max}=N(N-1)</math>; for directed graphs with self-connections allowed, <math>E_{\max}=N^2</math>. In the circumstance of a graph within which multiple edges may exist between a pair of vertices, <math>E_{\max}=\infty</math>.
网络的规模可以由节点的个数<math>N</math>，或者，少数情况下，连边的数量<math>E</math>（对于没有重边的连通图），连边的个数E的范围一般是从<math>N-1</math> （看做是一个树）到<math>E_{\max}</math> （看做是一个完全图）。在简单图的例子中（网络中在每对节点之间至多存在一条(无向)边，并且没有节点连向自己），可以计算<math>E_{\max}=\tbinom N2=N(N-1)/2</math>；对于有向图（没有自环self-connected的节点），<math>E_{\max}=N(N-1)</math>；对于有向图且允许存在自环的节点，<math>E_{\max}=N^2</math>.还有另外一种特殊情况就是一对节点之间存在重边， <math>E_{\max}=\infty</math>.
网络的规模可以由节点的个数<math>N</math>，或者，少数情况下，连边的数量<math>E</math>（对于没有重边的连通图），连边的个数E的范围一般是从<math>N-1</math> （看做是一个树）到<math>E_{\max}</math> （看做是一个完全图）。在简单图的例子中（网络中在每对节点之间至多存在一条(无向)边，并且没有节点连向自己），可以计算<math>E_{\max}=\tbinom N2=N(N-1)/2</math>；对于有向图（没有自环self-connected的节点），<math>E_{\max}=N(N-1)</math>；对于有向图且允许存在自环的节点，<math>E_{\max}=N^2</math>.还有另外一种特殊情况就是一对节点之间存在重边， <math>E_{\max}=\infty</math>.