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→Incidence matrix
:<math>a_{ij} = \left\{ \begin{matrix} 1 & \mathrm{if} ~ v_i \in e_j \\ 0 & \mathrm{otherwise}. \end{matrix} \right.</math>
:<math>a_{ij} = \left\{ \begin{matrix} 1 & \mathrm{if} ~ v_i \in e_j \\ 0 & \mathrm{otherwise}. \end{matrix} \right.</math>
The [[transpose]] <math>A^t</math> of the [[incidence (geometry)|incidence]] matrix defines a hypergraph <math>H^* = (V^*,\ E^*)</math> called the '''dual''' of <math>H</math>, where <math>V^*</math> is an ''m''-element set and <math>E^*</math> is an ''n''-element set of subsets of <math>V^*</math>. For <math>v^*_j \in V^*</math> and <math>e^*_i \in E^*, ~ v^*_j \in e^*_i</math> [[if and only if]] <math>a_{ij} = 1</math>.
The [[transpose]] <math>A^t</math> of the [[incidence (geometry)|incidence]] matrix defines a hypergraph <math>H^* = (V^*,\ E^*)</math> called the '''dual''' of <math>H</math>, where <math>V^*</math> is an ''m''-element set and <math>E^*</math> is an ''n''-element set of subsets of <math>V^*</math>. For <math>v^*_j \in V^*</math> and <math>e^*_i \in E^*, ~ v^*_j \in e^*_i</math> [[if and only if]] <math>a_{ij} = 1</math>.
分别设 <math>V = \{v_1, v_2, ~\ldots, ~ v_n\}</math>， <math>E = \{e_1, e_2, ~ \ldots ~ e_m\}</math>。
分别设 <math>V = \{v_1, v_2, ~\ldots, ~ v_n\}</math>， <math>E = \{e_1, e_2, ~ \ldots ~ e_m\}</math>。
每一个超图都有一个 <math>n \times m</math>[[关联矩阵]]<math>A = (a_{ij})</math>其为：<math>a_{ij} = \left\{ \begin{matrix} 1 & \mathrm{if} ~ v_i \in e_j \\ 0 & \mathrm{otherwise}. \end{matrix} \right.</math>
每一个超图都有一个 <math>n \times m</math>[[关联矩阵]]<math>A = (a_{ij})</math>其为：<math>a_{ij} = \left\{ \begin{matrix} 1 & \mathrm{if} ~ v_i \in e_j \\ 0 & \mathrm{otherwise}. \end{matrix} \right.</math>
其关联矩阵的[[转设]] <math>A^t</math>定义了 <math>H^* = (V^*,\ E^*)</math>称为<math>H</math>的'''对偶'''，其中<math>V^*</math>是一个''m''元集合 <math>E^*</math>是一个<math>V^*</math>子集的''n''元集合。
对于<math>v^*_j \in V^*</math> 和 <math>e^*_i \in E^*, ~ v^*_j \in e^*_i</math> [[当且仅当]] <math>a_{ij} = 1</math>。
==Hypergraph coloring==
==Hypergraph coloring==