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incidence_matrix [2014/02/08 02:03] nikolaj |
incidence_matrix [2014/03/21 11:11] |
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| - | ===== Incidence matrix ===== | ||
| - | ==== Set ==== | ||
| - | | @#88DDEE: $n_v,m_e\in \mathbb N$ | | ||
| - | |||
| - | | @#FFBB00: $ M\in \mathrm{it}(n_v,m_e) $ | | ||
| - | |||
| - | | @#55EE55: $ \mathrm{Matrix}(n_v,m_e,\{0,1,2\}) $ | | ||
| - | |||
| - | | @#FFFDDD: $i\in\mathrm{range}(n_v)$ | | ||
| - | |||
| - | | @#55EE55: $\sum_{j=1}^{m_e} M_{ij}=2 $ | | ||
| - | |||
| - | ==== 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. | ||
| - | |||
| - | Every incidence matrix corresponds to (a representative of the isomorphism class of) a [[finite undirected graph]]. | ||
| - | ==== Parents ==== | ||
| - | === Subset of === | ||
| - | [[Matrix]] | ||
