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undirected_graph [2014/02/09 20:51] nikolaj |
undirected_graph [2014/02/10 23:16] nikolaj |
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| In the above definition, the set $E=\{a,b,\dots\}$ in $\langle E,\psi\rangle$ is any set whos elements then each label an edge, e.g. $\psi(a)=\{v,w\}$. | In the above definition, the set $E=\{a,b,\dots\}$ in $\langle E,\psi\rangle$ is any set whos elements then each label an edge, e.g. $\psi(a)=\{v,w\}$. | ||
| - | Instead, one can also define a graph using a [[multiset]] $\langle E_\mathrm{ends},m\rangle$ where $E_\mathrm{ends}=\{\{v,w\},\{u,w\},\dots\}$ is itself a set of endpoints and $m:E_\mathrm{ends}\to\mathbb N$ counts the number of instances such a pair is part of the graph. The definitions are of course practically equivalent, but the definition with $\psi$ de-emphasises the focus on "$v$ and $w$ from $V$ are things which are connected" in favor of "$a$ is something from $E$ which connects the things $v$ and $w$ from $V$". | + | Instead, one can also define a graph using a [[multiset]] $\langle E_\mathrm{ends},m\rangle$ where $E_\mathrm{ends}=\{\{v,w\},\{u,w\},\dots\}$ is itself a set of endpoints and $m:E_\mathrm{ends}\to\mathbb N$ counts the number of instances such a pair is part of the graph. The definitions are of course practically equivalent, the definition above with $\psi$ de-emphasises the focus on "$v$ and $w$ from $V$ are things which are connected" in favor of "$a$ is something from $E$ which connects the things $v$ and $w$ from $V$". |
| ==== Parents ==== | ==== Parents ==== | ||
| === Subset of === | === Subset of === | ||
