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Drawing hasse diagram in Graphviz

Last updated at 2019-06-08Posted at 2019-06-01

Drawing Hasse diagram in Graphviz

There is also an opinion to do in TikZ.

𝕾₃ - Symmetric group (order 6)

𝕾₃(called S three)
|𝕾₃| = 3! = 6
𝕾₃ is not a commutative group.

The multiplication table

x_∘_y	e = ()	f = (1 2 3)	g = (1 3 2)	p = (1 2)	q = (2 3)	r = (1 3)
e=()	e=()	f=(1 2 3)	g=(1 3 2)	p=(1 2)	q=(2 3)	r=(1 3)
f=(1 2 3)	f=(1 2 3)	g=(1 3 2)	e=()	r=(1 3)	p=(1 2)	q=(2 3)
g=(1 3 2)	g=(1 3 2)	e=()	f=(1 2 3)	q=(2 3)	r=(1 3)	p=(1 2)
p=(1 2)	p=(1 2)	q=(2 3)	r=(1 3)	e=()	f=(1 2 3)	g=(1 3 2)
q=(2 3)	q=(2 3)	r=(1 3)	p=(1 2)	g=(1 3 2)	e=()	f=(1 2 3)
r=(1 3)	r=(1 3)	p=(1 2)	q=(2 3)	f=(1 2 3)	g=(1 3 2)	e=()

no adjusting

Around {e} is something like a barrier (like the AT field). I would like to strip off such things.

graph {
  layout = dot
  rankdir = TB
  node [ shape="none" ]

  G [label="{e, f, g, p, q, r}"]

  e_p [label="{e, p}"]
  e_q [label="{e ,q}"]
  e_r [label="{e, r}"]
  e_f_g [label="{e, f, g}"]
  { rank=same; e_p; e_q; e_r; e_f_g; }

  e [ label="{e}" ]

  G -- {e_p, e_q, e_r, e_f_g}
  {e_p, e_q, e_r, e_f_g} -- e
}

customize node size and spacing

If fixedsize = true, you can customize the node width and height parameters.
You can customize the margin between the upper and lower rank with the ranksep parameter.

graph {
  layout = dot
  rankdir = TB
  graph [ pad="0.2", ranksep="0.4", nodesep="0.2", splines="line" ];
  node [ shape="none" ]

  G [
    label=<{<I>e</I>, <I>f</I>, <I>g</I>, <I>p</I>, <I>q</I>, <I>r</I>}>,
    fixedsize=true, width=1.75, height=0.25
  ]

  e_p [label=<{<I>e</I>, <I>p</I>}>, fixedsize=true, width=0.63, height=0.25]
  e_q [label=<{<I>e</I>, <I>q</I>}>, fixedsize=true, width=0.63, height=0.25]
  e_r [label=<{<I>e</I>, <I>r</I>}>, fixedsize=true, width=0.63, height=0.25]
  e_f_g [
    label=<{<I>e</I>, <I>f</I>, <I>g</I>}>,
    fixedsize=true, width=0.83, height=0.25
  ]
  { rank=same; e_p; e_q; e_r; e_f_g; }

  e [ label=<{<I>e</I>}>, fixedsize=true, width=0.35, height=0.25 ]

  G -- {e_p, e_q, e_r, e_f_g} [ headport=n, tailport=s ]
  {e_p, e_q, e_r, e_f_g} -- e [ headport=n, tailport=s ]
}

subgroup of 𝕾₄ - Symmetric group (order 24)

𝕾₄ = {e=(), f=(A B C D), g=(A C)(B D), h=(A D C B), i=(A C), j=(B D), k=(A B)(C D), l=(A D)(B C)}

|𝕾₄|=4!=24

graph {
  layout = dot
  rankdir = TB
  graph [ pad="0.1", ranksep="0.4", nodesep="0.2", splines="line" ];
  node [ shape="none", fixedsize=true, width=1.1, height=0.25 ]

  G [ label=<<I>G</I>>, fixedsize=true, width=0.2, height=0.22 ]

  e_i_j_g [
    label=<{<I>e</I>, <I>g</I>, <I>i</I>, <I>j</I>}>,
    fixedsize=true, width=1.1, height=0.25
  ]
  e_f_g_h [
    label=<{<I>e</I>, <I>g</I>, <I>f</I>, <I>h</I>}>,
    fixedsize=true, width=1.15, height=0.25
  ]
  e_k_g_l [label=<{<I>e</I>, <I>g</I>, <I>k</I>, <I>l</I>}>,
    fixedsize=true, width=1.18, height=0.25
  ]
  { rank=same; e_i_j_g; e_f_g_h; e_k_g_l; }

  e_i [label=<{<I>e</I>, <I>i</I>}>, fixedsize=true, width=0.59, height=0.25]
  e_j [label=<{<I>e</I>, <I>j</I>}>, fixedsize=true, width=0.59, height=0.25]
  e_g [label=<{<I>e</I>, <I>g</I>}>, fixedsize=true, width=0.63, height=0.25]
  e_k [label=<{<I>e</I>, <I>k</I>}>, fixedsize=true, width=0.63, height=0.25]
  e_l [label=<{<I>e</I>, <I>l</I>}>, fixedsize=true, width=0.59, height=0.25]
  { rank=same; e_i; e_j; e_g; e_k; e_l; }

  e [ label=<{<I>e</I>}>, fixedsize=true, width=0.4, height=0.25 ]

  G -- {e_i_j_g, e_f_g_h, e_k_g_l}

  e_i_j_g -- {e_i, e_j, e_g}
  e_f_g_h -- {e_g}
  e_k_g_l -- {e_g, e_k, e_l}

  {e_i, e_j, e_g, e_k, e_l} -- e [tailport=s]
}

Mapping example

Software named Graphviz was born to automatically arrange nodes of graph structure. Inconsistent use of not automatically placing on it.

no adjusting

Oh my God. We do not want to change the order.

digraph {
  layout = dot
  rankdir = LR
  splines=true;
  subgraph cluster_0 {
    graph [ label=X ]
    s1 [label="1"]
    s2 [label="2"]
    s3 [label="3"]
  }
  subgraph cluster_1 {
    graph [ label=X ]
    t1 [label="1"]
    t2 [label="2"]
    t3 [label="3"]
  }
  subgraph cluster_2 {
    graph [ label=X ]
    d1 [label="1"]
    d2 [label="2"]
    d3 [label="3"]
  }

  s1 -> t1 -> d3
  s2 -> t3 -> d1
  s3 -> t2 -> d2
}

Arrange the order with `constraint=false`

By setting constraint = false, edge combination will not move the placement of nodes.
But, ...Perish them!

digraph {
  layout = dot
  rankdir = LR
  splines=true;
  // compound=true
  // graph [ newrank=true; ]
  subgraph cluster_0 {
    graph [ label=X ]
    s1 [label="1"]
    s2 [label="2"]
    s3 [label="3"]
    // { rank=same; s1; s2; s3; }
  }
  subgraph cluster_1 {
    graph [ label=X ]
    t1 [label="1"]
    t2 [label="2"]
    t3 [label="3"]
    // { rank=same; t1; t2; t3; }
  }
  subgraph cluster_2 {
    graph [ label=X ]
    d1 [label="1"]
    d2 [label="2"]
    d3 [label="3"]
    // { rank=same; d1; d2; d3; }
  }
  // s1 -> t1 -> d1[style=invis]

  s1 -> t1 -> d3 [constraint=false]
  s2 -> t3 -> d1 [constraint=false]
  s3 -> t2 -> d2 [constraint=false]
}

adjust rank

If you adjust the rank in the cluster rankdir = LR will align vertically.
Adjust the order between clusters with s1 -> t1 -> d1[style=invis].
However, these oval in number like a pig has abundance of flesh. This is not beautiful. I would like to kill them after consultation.

digraph {
  layout = dot
  rankdir = LR
  splines=true;
  compound=true
  graph [ newrank=true; ]
  subgraph cluster_0 {
    graph [ label=X ]
    s1 [label="1"]
    s2 [label="2"]
    s3 [label="3"]
    { rank=same; s1; s2; s3; }
  }
  subgraph cluster_1 {
    graph [ label=X ]
    t1 [label="1"]
    t2 [label="2"]
    t3 [label="3"]
    { rank=same; t1; t2; t3; }
  }
  subgraph cluster_2 {
    graph [ label=X ]
    d1 [label="1"]
    d2 [label="2"]
    d3 [label="3"]
    { rank=same; d1; d2; d3; }
  }
  s1 -> t1 -> d1[style=invis]

  s1 -> t1 -> d3 [constraint=false]
  s2 -> t3 -> d1 [constraint=false]
  s3 -> t2 -> d2 [constraint=false]
}

eden

adjust size and set background color

digraph {
  layout = dot
  rankdir = LR
  splines=true;
  node [
    shape=circle, style="filled,solid", fillcolor="#dd6060",
    width=0.25, fixedsize=true,
    color="#0d0ee0d",  # node border color (X11 or HTML colors)
    fontsize=12, fontcolor="black"
  ]
  edge [
    arrowhead=vee, color="#8b0000"
  ]
  subgraph cluster_0 {
    graph [
      label=<<I>X</I>>,fontcolor="#5A3A1A",
      style="filled,solid,rounded",shape="oval",
      fillcolor="#f5f5dc",color="#d5d5ac"
    ]
    s1 [label="1"]
    s2 [label="2"]
    s3 [label="3"]
    { rank=same; s1; s2; s3; }
  }
  subgraph cluster_1 {
    graph [
      label=<<I>X</I>>,fontcolor="#5A3A1A",
      style="filled,solid,rounded",shape="oval",
      fillcolor="#f5f5dc",color="#d5d5ac"
    ]
    t1 [label="1"]
    t2 [label="2"]
    t3 [label="3"]
    { rank=same; t1; t2; t3; }
  }
  subgraph cluster_2 {
    graph [
      label=<<I>X</I>>,fontcolor="#5A3A1A",
      style="filled,solid,rounded",shape="oval",
      fillcolor="#f5f5dc",color="#d5d5ac"
    ]
    d1 [label="1"]
    d2 [label="2"]
    d3 [label="3"]
    { rank=same; d1; d2; d3; }
  }
  s1 -> t1 -> d1[style=invis]

  s1 -> t1 -> d3 [constraint=false]
  s2 -> t3 -> d1 [constraint=false]
  s3 -> t2 -> d2 [constraint=false]
}

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Drawing hasse diagram in Graphviz

Drawing Hasse diagram in Graphviz

𝕾3 - Symmetric group (order 6)

no adjusting

customize node size and spacing

subgroup of 𝕾4 - Symmetric group (order 24)

Mapping example

no adjusting

Arrange the order with constraint=false

adjust rank

eden

𝕾₃ - Symmetric group (order 6)

subgroup of 𝕾₄ - Symmetric group (order 24)

Arrange the order with `constraint=false`