零模型
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In mathematics, for example in the study of statistical properties of graphs, a null model is a type of random object that matches one specific object in some of its features, or more generally satisfies a collection of constraints, but which is otherwise taken to be an unbiasedly random structure. The null model is used as a term of comparison, to verify whether the object in question displays some non-trivial features (properties that wouldn't be expected on the basis of chance alone or as a consequence of the constraints), such as community structure in graphs. An appropriate null model behaves in accordance with a reasonable null hypothesis for the behavior of the system under investigation.
In mathematics, for example in the study of statistical properties of graphs, a null model is a type of random object that matches one specific object in some of its features, or more generally satisfies a collection of constraints, but which is otherwise taken to be an unbiasedly random structure. The null model is used as a term of comparison, to verify whether the object in question displays some non-trivial features (properties that wouldn't be expected on the basis of chance alone or as a consequence of the constraints), such as community structure in graphs. An appropriate null model behaves in accordance with a reasonable null hypothesis for the behavior of the system under investigation.
在数学中，例如在图的统计特性的研究中，空模型是一种随机对象，它在某些特征上与某一特定对象相匹配，或者更一般地满足一组约束，但是在其他方面被认为是一个无偏的随机结构。空模型被用作一个比较的术语，用来验证所讨论的对象是否显示出一些非平凡的特征(不会仅仅基于偶然性或作为约束的结果而期望的属性) ，例如图中的社区结构。一个适当的零模型的行为符合一个合理的零假设的行为系统的调查。
One null model of utility in the study of complex networks is that proposed by Newman and Girvan, consisting of a randomized version of an original graph [math]\displaystyle{ G }[/math], produced through edges being rewired at random, under the constraint that the expected degree of each vertex matches the degree of the vertex in the original graph.[1]
One null model of utility in the study of complex networks is that proposed by Newman and Girvan, consisting of a randomized version of an original graph G, produced through edges being rewired at random, under the constraint that the expected degree of each vertex matches the degree of the vertex in the original graph.
在复杂网络的研究中，Newman 和 Girvan 提出了一种零效用模型，该模型由原始图 G 的随机化版本组成，通过随机重新布线生成边，约束条件是每个顶点的期望度与原始图中顶点的度相匹配。
The null model is the basic concept behind the definition of modularity, a function which evaluates the goodness of partitions of a graph into clusters. In particular, given a graph [math]\displaystyle{ G }[/math] and a specific community partition [math]\displaystyle{ \sigma:V(G)\rightarrow \{1,...,b\} }[/math] (an assignment of a community-index [math]\displaystyle{ \sigma(v) }[/math] (here taken as an integer from [math]\displaystyle{ 1 }[/math] to [math]\displaystyle{ b }[/math]) to each vertex [math]\displaystyle{ v\in V(G) }[/math] in the graph), the modularity measures the difference between the number of links from/to each pair of communities, from that expected in a graph that is completely random in all respects other than the set of degrees of each of the vertices (the degree sequence). In other words, the modularity contrasts the exhibited community structure in [math]\displaystyle{ G }[/math] with that of a null model, which in this case is the configuration model (the maximally random graph subject to a constraint on the degree of each vertex).
The null model is the basic concept behind the definition of modularity, a function which evaluates the goodness of partitions of a graph into clusters. In particular, given a graph G and a specific community partition \sigma:V(G)\rightarrow \{1,...,b\} (an assignment of a community-index \sigma(v) (here taken as an integer from 1 to b) to each vertex v\in V(G) in the graph), the modularity measures the difference between the number of links from/to each pair of communities, from that expected in a graph that is completely random in all respects other than the set of degrees of each of the vertices (the degree sequence). In other words, the modularity contrasts the exhibited community structure in G with that of a null model, which in this case is the configuration model (the maximally random graph subject to a constraint on the degree of each vertex).
零模型是模块化定义背后的基本概念，它是一个评价图划分成簇的优劣程度的函数。特别是，给定一个图 G 和一个特定的社区划分 sigma: V (G) right tarrow {1，... ，b }(一个社区索引 sigma (v)的赋值(这里取为一个从1到 b 的整数)到图 V (G)中的每个顶点 v) ，模块化度量了从/到每对社区的链接数量之间的差异，从一个在所有方面都是完全随机的图中的期望值，而不是每个顶点的度集(度序列)。换句话说，模块性将 G 中显示的社区结构与空模型的结构进行了对比，在这种情况下，空模型是配置模型(最大随机图受到每个顶点度的约束)。
See also
- Null hypothesis
See also
- Null hypothesis
References
- ↑ M.E.J, Newman; M.Girvan (2004). "Finding and evaluating community structure in networks". Phys. Rev. E. 69 (2): 026113. arXiv:cond-mat/0308217. Bibcode:2004PhRvE..69b6113N. doi:10.1103/physreve.69.026113. PMID 14995526.
Category:Graph theory
分类: 图论
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