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第353行： + − 在引用图中，顶点是只有一个出版日期的文档。边代表从一个文档的参考书目到其他必要的早期文档的引用。经典的例子来自于学术论文之间的引用，正如1965年德瑞克·约翰·德索拉·普莱斯在《科学论文网络》一文中指出的那样，他继续创造了引用网络的第一个模型---- 价格模型。在这种情况下，一篇论文的引文数量就是引文网络相应顶点的度数。这是21引文分析的一项重要措施。法院判决提供了另一个例子，因为法官通过回顾以前案件中作出的其他判决来支持他们在一个案件中的结论。最后一个例子是专利，必须提到先前的技术，先前的专利，这是有关当前的专利权利主张。通过考虑有向无环图的特殊性质，可以利用网络分析方法分析引文网络。例如，传递减法对不同应用中的引用分布提供了新的见解，突出了不同上下文中引用网络形成机制的明显差异。另一种技术是主路径分析，它跟踪引文链接，并提出给定引文图中最重要的引文链。+ + + − The Price model is too simple to be a realistic model of a citation network but it is simple enough to allow for analytic solutions for some of its properties. Many of these can be found by using results derived from the undirected version of the Price model, the Barabási–Albert model. However, since Price's model gives a directed acyclic graph, it is a useful model when looking for analytic calculations of properties unique to directed acyclic graphs. For instance,+ − 普莱斯模型过于简单，不可能成为引文网络的现实模型，但它足够简单，可以为其某些属性提供分析解。其中许多问题可以通过使用从价格模型(Barabási-Albert 模型)的无向版本得出的结果来找到。然而，由于 Price 的模型给出了一个有向无环图，所以在寻找有向无圈图所特有的性质的解析计算时，它是一个很有用的模型。比如说,+
→Causal structures 因果结构
[[File:Pert chart colored.svg|thumb|PERT chart for a project with five milestones (labeled 10–50) and six tasks (labeled A–F). There are two critical paths, ADF and BC.]]
[[File:Pert chart colored.svg|thumb|PERT chart for a project with five milestones (labeled 10–50) and six tasks (labeled A–F). There are two critical paths, ADF and BC.]]
=== Citation graphs 引用图 ===
In a citation graph the vertices are documents with a single publication date. The edges represent the citations from the bibliography of one document to other necessarily earlier documents. The classic example comes from the citations between academic papers as pointed out in the 1965 article "Networks of Scientific Papers" by Derek J. de Solla Price who went on to produce the first model of a citation network, the Price model. In this case the citation count of a paper is just the in-degree of the corresponding vertex of the citation network. This is an important measure in citation analysis. Court judgements provide another example as judges support their conclusions in one case by recalling other earlier decisions made in previous cases. A final example is provided by patents which must refer to earlier prior art, earlier patents which are relevant to the current patent claim. By taking the special properties of directed acyclic graphs into account, one can analyse citation networks with techniques not available when analysing the general graphs considered in many studies using network analysis. For instance transitive reduction gives a new insights into the citation distributions found in different applications highlighting clear differences in the mechanisms creating citations networks in different contexts. Another technique is main path analysis, which traces the citation links and suggests the most significant citation chains in a given citation graph.
In a citation graph the vertices are documents with a single publication date. The edges represent the citations from the bibliography of one document to other necessarily earlier documents. The classic example comes from the citations between academic papers as pointed out in the 1965 article "Networks of Scientific Papers" by Derek J. de Solla Price who went on to produce the first model of a citation network, the Price model. In this case the citation count of a paper is just the in-degree of the corresponding vertex of the citation network. This is an important measure in citation analysis. Court judgements provide another example as judges support their conclusions in one case by recalling other earlier decisions made in previous cases. A final example is provided by patents which must refer to earlier prior art, earlier patents which are relevant to the current patent claim. By taking the special properties of directed acyclic graphs into account, one can analyse citation networks with techniques not available when analysing the general graphs considered in many studies using network analysis. For instance transitive reduction gives a new insights into the citation distributions found in different applications highlighting clear differences in the mechanisms creating citations networks in different contexts. Another technique is main path analysis, which traces the citation links and suggests the most significant citation chains in a given citation graph.
在引用图（英语：citation graph）中， 每个顶点代表单篇著作，边代表著作之间的引用关系。1965年普莱斯的文章“科学文献的网络”是使用引用图的一个经典例子。[49]在引用图中，每篇论文的引用次数（英语：Citation impact）为对应顶点的入度。这是引文分析中的一种重要的展示方式。另一个例子是法律裁判中，法官通过引用过往案例中的判决来支持他们的结论。引用图亦可以用来描绘专利，因为专利必须要提及现有技术，即已经公开的并且和本专利有关的先前专利。
The Price model is too simple to be a realistic model of a citation network but it is simple enough to allow for analytic solutions for some of its properties. Many of these can be found by using results derived from the undirected version of the Price model, the Barabási–Albert model. However, since Price's model gives a directed acyclic graph, it is a useful model when looking for analytic calculations of properties unique to directed acyclic graphs. For instance,
相较于网络科学中对一般图的研究，有向无环图的独特性质可以被用来作深层次分析。例如，传递规约可以呈现引用在不同应用领域的分布情况，这突出了不同领域中不同的引用网构造机制。[50]引用图的衍生概念还有主干道路分析（英语：Main path analysis），即对引用图中最显著的一条路径的分析。
价格模型太简单了，不可能成为引文网络的现实模型，但它足够简单，可以为它的某些特性提供解析解。其中许多可以通过使用价格模型的无向版本Barab得出的结果来发现ási–阿尔伯特模型。然而，由于Price的模型给出了一个有向无环图，因此在寻找有向无环图所特有的性质的解析计算时，它是一个有用的模型。例如，从添加到网络中的第n个节点到网络中的第一个节点的最长路径的长度按[52]{\displaystyle\ln（n）}
缩放。