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DegreeGraphDistribution[dlist]

表示顶点度为 dlist 的图的度分布.

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DegreeGraphDistribution

DegreeGraphDistribution[dlist]

表示顶点度为 dlist 的图的度分布.

更多信息和选项

范例

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基本范例  (2)

生成随机图：

Wolfram Language code: RandomGraph[DegreeGraphDistribution[{4, 4, 3, 3, 2, 2}]]

全局集群系数的概率密度函数：

Wolfram Language code: 𝒟[n_, k_] := GraphPropertyDistribution[GlobalClusteringCoefficient[g], gDegreeGraphDistribution[ConstantArray[k, n]]]
Wolfram Language code: SmoothHistogram[Table[RandomVariate[𝒟[20, k], 500], {k, 5, 8}], Automatic, "PDF", Filling -> Axis]

范围  (3)

生成简单无向图：

Wolfram Language code: RandomGraph[DegreeGraphDistribution[{4, 4, 2, 2, 1, 1}]]

生成一组伪随机图：

Wolfram Language code: RandomGraph[DegreeGraphDistribution[{3, 3, 2, 2, 1, 1}], 4]

计算概率和统计属性：

Wolfram Language code: 𝒟 = GraphPropertyDistribution[Length[First[ConnectedComponents[g]]] / VertexCount[g], gDegreeGraphDistribution[{3, 3, 2, 2, 1, 1}]];
Wolfram Language code: NProbability[x > 0.95, x𝒟]

应用  (2)

在对流感爆发的医学研究中，每个受试者都报告了该组内潜在的传染性相互作用的数量. 模拟交互网络：

Wolfram Language code: 𝒢 = DegreeGraphDistribution[{2, 4, 4, 4, 3, 3, 2}];
Wolfram Language code: RandomGraph[𝒢, 4]

求受试者 1 与受试者 2 交互的概率：

Wolfram Language code: NProbability[x == 1, xGraphPropertyDistribution[Boole[EdgeQ[g, 12]], g𝒢]]

分析一个网络是否根据度的图分布绘制：

Wolfram Language code: g = ExampleData[{"NetworkGraph", "ZacharyKarateClub"}]
Wolfram Language code: 𝒢 = DegreeGraphDistribution[VertexDegree[g]];

比较经验和理论的基本属性：

Wolfram Language code: {VertexCount[g], EdgeCount[g]}
Wolfram Language code: Subscript[𝒟, 1] = GraphPropertyDistribution[VertexCount[h], h𝒢]; Subscript[𝒟, 2] = GraphPropertyDistribution[EdgeCount[h], h𝒢]; {Mean[Subscript[𝒟, 1]], Mean[Subscript[𝒟, 2]]}

经验和理论全局聚类系数：

Wolfram Language code: N[GlobalClusteringCoefficient[g]]
Wolfram Language code: 𝒟 = GraphPropertyDistribution[GlobalClusteringCoefficient[h], h𝒢]; N[Mean[𝒟]]

属性和关系  (7)

顶点数目分布：

Wolfram Language code: 𝒟[dlist_] := GraphPropertyDistribution[VertexCount[g], gDegreeGraphDistribution[dlist]]
Wolfram Language code: 𝒟[{5, 2, 2, 5, 3, 4, 3}]

边数分布：

Wolfram Language code: 𝒟[dlist_] := GraphPropertyDistribution[EdgeCount[g], gDegreeGraphDistribution[dlist]]
Wolfram Language code: 𝒟[{5, 2, 2, 5, 3, 4, 3}]

顶点度数分布：

Wolfram Language code: dlist = {14, 13, 12, 11, 11, 11, 10, 10, 10, 9, 8, 8, 7, 6, 5, 5, 5, 5, 5, 5};
Wolfram Language code: f[g_ ? GraphQ] := RandomChoice[VertexDegree[g]]
Wolfram Language code: RandomVariate[GraphPropertyDistribution[f[g], gDegreeGraphDistribution[dlist]], 10]

概率密度函数：

Wolfram Language code: 𝒟 = EmpiricalDistribution[dlist];
Wolfram Language code: DiscretePlot[PDF[𝒟, x], {x, 0, 15}, ExtentSize -> 1 / 2]

顶点度的均值：

Wolfram Language code: Mean[𝒟]

图的度序列和总是偶数：

Wolfram Language code: ds1 = {3, 3, 2, 2, 1, 1}; Total[ds1]
Wolfram Language code: RandomGraph[DegreeGraphDistribution[ds1]]

具有奇数总度数的度序列无法实现为一个图：

Wolfram Language code: ds2 = {3, 3, 2, 2, 2, 1}; Total[ds2]
Wolfram Language code: RandomGraph[DegreeGraphDistribution[ds2]]

是简单图的度序列，当且仅当 是：

Wolfram Language code: g = RandomGraph[{7, 9}]

排序度序列：

Wolfram Language code: d = Sort[VertexDegree[g], Greater]

不使用最大度顶点重建度序列：

Wolfram Language code: Join[Take[d, {2, First[d] + 1}] - 1, Drop[d, First[d] + 1]]
Wolfram Language code: RandomGraph[DegreeGraphDistribution[%]]
Wolfram Language code: SimpleGraphQ /@ {g, %}

具有相同的度序列的图可以是非同态的：

Wolfram Language code: g = RandomGraph[{10, 12}]
Wolfram Language code: IsomorphicGraphQ[g, #]& /@ Table[RandomGraph[DegreeGraphDistribution[VertexDegree[g]]], {10}]

具有不同度数的度序列使用具有自环的图实现：

Wolfram Language code: RandomGraph[DegreeGraphDistribution[Range[7]]]
Wolfram Language code: LoopFreeGraphQ[%]

巧妙范例  (1)

随机着色的顶点：

Wolfram Language code: HighlightGraph[RandomGraph[DegreeGraphDistribution[Table[3, {10 ^ 2}]], VertexSize -> {"Scaled", 0.02}], Table[Style[i, RandomChoice[ColorData[45, "ColorList"]]], {i, 10 ^ 2}]]
Wolfram Research (2010)，DegreeGraphDistribution，Wolfram 语言函数，https://reference.wolfram.com/language/ref/DegreeGraphDistribution.html.

文本

Wolfram Research (2010)，DegreeGraphDistribution，Wolfram 语言函数，https://reference.wolfram.com/language/ref/DegreeGraphDistribution.html.

CMS

Wolfram 语言. 2010. "DegreeGraphDistribution." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/DegreeGraphDistribution.html.

APA

Wolfram 语言. (2010). DegreeGraphDistribution. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/DegreeGraphDistribution.html 年

BibTeX

@misc{reference.wolfram_2026_degreegraphdistribution, author="Wolfram Research", title="{DegreeGraphDistribution}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/DegreeGraphDistribution.html}", note=[Accessed: 14-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_degreegraphdistribution, organization={Wolfram Research}, title={DegreeGraphDistribution}, year={2010}, url={https://reference.wolfram.com/language/ref/DegreeGraphDistribution.html}, note=[Accessed: 14-September-2026]}