Hasse diagram

If $(A,\le )$ is a finite poset, then it can be represented by a Hasse diagram, which is a graph whose vertices are elements of $A$ and the edges correspond to the covering relation. More precisely an edge from $x\in A$ to $y\in A$ is present if

• .

• There is no $z\in A$ such that and . (There are no in-between elements.)

If , then in $y$ is drawn higher than $x$. Because of that, the direction of the edges is never indicated in a Hasse diagram.

Example: If $A=𝒫(\{1,2,3\})$, the power set of $\{1,2,3\}$, and $\le$is the subset relation $\subseteq$, then Hasse diagram is

Even though (since $\{3\}\subset \{1,2,3\}$), there is no edge directly between them because there are inbetween elements:$\{2,3\}$ and $\{1,3\}$. However, there still remains an indirect path from $\{3\}$ to $\{1,2,3\}$.