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incidence_matrix [2014/02/08 02:02] nikolaj |
incidence_matrix [2014/03/21 11:11] (current) |
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| ===== Incidence matrix ===== | ===== Incidence matrix ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#88DDEE: $n_v,m_e\in \mathbb N$ | | + | | @#55CCEE: context | @#55CCEE: $n_v,m_e\in \mathbb N$ | |
| - | | @#FFBB00: $ M\in \mathrm{it}(n_v,m_e) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ M\in \mathrm{it}(n_v,m_e) $ | |
| - | | @#55EE55: $ \mathrm{Matrix}(n_v,m_e,\{0,1,2\}) $ | | + | | @#55EE55: postulate | @#55EE55: $ \mathrm{Matrix}(n_v,m_e,\{0,1,2\}) $ | |
| - | | @#FFFDDD: $i\in\mathrm{range}(n_v)$ | | + | | @#FFFDDD: for all | @#FFFDDD: $i\in\mathrm{range}(n_v)$ | |
| - | | @#55EE55: $\sum_{j=1}^{m_e} M_{ij}=2 $ | | + | | @#55EE55: postulate | @#55EE55: $\sum_{j=1}^{m_e} M_{ij}=2 $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| The index $i$ in $M_{ij}$ labels the vertices and the index $j$ labels the edges. The definition says that every edge has exactly two endpoints. | The index $i$ in $M_{ij}$ labels the vertices and the index $j$ labels the edges. The definition says that every edge has exactly two endpoints. | ||
| + | |||
| + | Every incidence matrix corresponds to (a representative of the isomorphism class of) a [[finite undirected graph]]. | ||
| ==== Parents ==== | ==== Parents ==== | ||
| === Subset of === | === Subset of === | ||
| [[Matrix]] | [[Matrix]] | ||
| + | === Related === | ||
| + | [[Finite undirected graph]] | ||
