Rank between source and sink

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5

That’s cause 0.5 is the default.

0.1 did it.

Here is the final working solution:

digraph subset {
  ranksep=0.1
  node [shape="square", width=0.5, label=""]
  node [shape="square", label=""]
  edge [style="invis"]

  subgraph fullset {
    rank="source"

    fs0 [label="0"]
    fs1 [label="1"]
    fs2 [label="2"]
    fs3 [label="3"]
    fs4 [label="4"]
    fs5 [label="5"]
    fs6 [label="6"]
    fs7 [label="7"]

    fs0 -> fs1 -> fs2 -> fs3 -> fs4 -> fs5 -> fs6 -> fs7
  }

  subgraph rn {
    rank="same"
    node [shape="none", width=0.5]

    r0 [label="1"]
    r1 [label="0"]
    r2 [label="0"]
    r3 [label="1"]
    r4 [label="0"]
    r5 [label="1"]
    r6 [label="1"]
    r7 [label="0"]

    r0 -> r1 -> r2 -> r3 -> r4 -> r5 -> r6 -> r7
  }

  subgraph subset {
    rank="sink"

    s0 [label="0"]
    s3 [label="3"]
    s5 [label="5"]
    s6 [label="6"]

    node [style="invis"]
    s1
    s2
    s4
    s7

    s0 -> s1 -> s2 -> s3 -> s4 -> s5 -> s6 -> s7
  }
}

final solution

Marking this as solution for completeness, but wouldn’t have arrived at this solution without @steveroush’s help.