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第111行： − == 网络性质 Network properties == − Often, networks have certain attributes that can be calculated to analyze the properties & characteristics of the network. The behavior of these network properties often define network models and can be used to analyze how certain models contrast to each other. Many of the definitions for other terms used in network science can be found in Glossary of graph theory. − − 通常，网络具有某些可计算的属性，用于分析网络的属性和特征。 这些网络属性的特征通常能定义网络模型，并可用于分析对比不同的模型。 网络科学中使用的其他术语的许多定义可以在[[图论术语表]]''Glossary of graph theory''中找到。 − − − − − − === 规模 === − 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>. −
→Network properties
== Network properties ==
== Network properties ==
Often, networks have certain attributes that can be calculated to analyze the properties & characteristics of the network. The behavior of these network properties often define [[network model]]s and can be used to analyze how certain models contrast to each other. Many of the definitions for other terms used in network science can be found in [[Glossary of graph theory]].
Often, networks have certain attributes that can be calculated to analyze the properties & characteristics of the network. The behavior of these network properties often define [[network model]]s and can be used to analyze how certain models contrast to each other. Many of the definitions for other terms used in network science can be found in [[Glossary of graph theory]].
=== Size ===
=== Size ===
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>.
=== Density ===
=== Density ===