How to manage distance between nodes in graphviz?

Question

I am trying to plot a graph with 3 levels of nodes, with equal distances between the levels. However, graphviz somehow decides that the distance between the middle level and the bottom one should be much larger than the distance between the top and middle level. Any way to fix this?

Here is my code:

digraph g{
    rankdir="LR";
    graph [pad="0.5", ranksep="0.525", nodesep="3"];
    splines=false;
    node[shape = square];
    edge[style=invis];
    subgraph cluster_3 {
        color=invis;
        a1->a2->a3->a4->a5->a6->a7;
    }
    subgraph cluster_2 {
        color=invis;
        a->b->c->d->e->f->g;
    }
    subgraph cluster_1 {
        color=invis;
        1->2->3->4->5->6->7;
    }
    "a1" [label="1'"];
    "a2" [label="2'"];
    "a3" [label="3'"];
    "a4" [label="4'"];
    "a5" [label="5'"];
    "a6" [label="6'"];
    "a7" [label="7'"];
    edge[style=solid, constraint=false];
    a->1[arrowhead=none, arrowtail=none];
    a->2[arrowhead=none, arrowtail=none];
    a->3[arrowhead=none, arrowtail=none];
    a->a1[arrowhead=none, arrowtail=none];
    a->a2[arrowhead=none, arrowtail=none];
    a->a3[arrowhead=none, arrowtail=none];
    b->1[arrowhead=none, arrowtail=none];
    b->3[arrowhead=none, arrowtail=none];
    b->7[arrowhead=none, arrowtail=none];
    b->a1[arrowhead=none, arrowtail=none];
    b->a3[arrowhead=none, arrowtail=none];
    b->a7[arrowhead=none, arrowtail=none];
    c->2[arrowhead=none, arrowtail=none];
    c->6[arrowhead=none, arrowtail=none];
    c->7[arrowhead=none, arrowtail=none];
    c->a2[arrowhead=none, arrowtail=none];
    c->a6[arrowhead=none, arrowtail=none];
    c->a7[arrowhead=none, arrowtail=none];
    d->1[arrowhead=none, arrowtail=none];
    d->4[arrowhead=none, arrowtail=none];
    d->7[arrowhead=none, arrowtail=none];
    d->a1[arrowhead=none, arrowtail=none];
    d->a4[arrowhead=none, arrowtail=none];
    d->a7[arrowhead=none, arrowtail=none];
    e->1[arrowhead=none, arrowtail=none];
    e->2[arrowhead=none, arrowtail=none];
    e->3[arrowhead=none, arrowtail=none];
    e->a1[arrowhead=none, arrowtail=none];
    e->a2[arrowhead=none, arrowtail=none];
    e->a3[arrowhead=none, arrowtail=none];
    f->1[arrowhead=none, arrowtail=none];
    f->4[arrowhead=none, arrowtail=none];
    f->7[arrowhead=none, arrowtail=none];
    f->a1[arrowhead=none, arrowtail=none];
    f->a4[arrowhead=none, arrowtail=none];
    f->a7[arrowhead=none, arrowtail=none];
    g->5[arrowhead=none, arrowtail=none];
    g->6[arrowhead=none, arrowtail=none];
    g->7[arrowhead=none, arrowtail=none];
    g->a5[arrowhead=none, arrowtail=none];
    g->a6[arrowhead=none, arrowtail=none];
    g->a7[arrowhead=none, arrowtail=none];
}

The output looks like this currently:

Answer 1

Just played around a bit and came up with the below graph, is this any closer to want to want?

digraph g{
    graph [pad="0.5", nodesep="1", ranksep="2"];
    splines="false";
    node[shape = square];
    edge[style=invis];
    a1->a->1
    a2->b->2
    a3->c->3
    a4->d->4
    a5->e->5
    a6->f->6
    a7->g->7

    "a1" [label="1'"];
    "a2" [label="2'"];
    "a3" [label="3'"];
    "a4" [label="4'"];
    "a5" [label="5'"];
    "a6" [label="6'"];
    "a7" [label="7'"];
    edge[style=solid, constraint=false];
    a->1[arrowhead=none, arrowtail=none];
    a->2[arrowhead=none, arrowtail=none];
    a->3[arrowhead=none, arrowtail=none];
    a->a1[arrowhead=none, arrowtail=none];
    a->a2[arrowhead=none, arrowtail=none];
    a->a3[arrowhead=none, arrowtail=none];
    b->1[arrowhead=none, arrowtail=none];
    b->3[arrowhead=none, arrowtail=none];
    b->7[arrowhead=none, arrowtail=none];
    b->a1[arrowhead=none, arrowtail=none];
    b->a3[arrowhead=none, arrowtail=none];
    b->a7[arrowhead=none, arrowtail=none];
    c->2[arrowhead=none, arrowtail=none];
    c->6[arrowhead=none, arrowtail=none];
    c->7[arrowhead=none, arrowtail=none];
    c->a2[arrowhead=none, arrowtail=none];
    c->a6[arrowhead=none, arrowtail=none];
    c->a7[arrowhead=none, arrowtail=none];
    d->1[arrowhead=none, arrowtail=none];
    d->4[arrowhead=none, arrowtail=none];
    d->7[arrowhead=none, arrowtail=none];
    d->a1[arrowhead=none, arrowtail=none];
    d->a4[arrowhead=none, arrowtail=none];
    d->a7[arrowhead=none, arrowtail=none];
    e->1[arrowhead=none, arrowtail=none];
    e->2[arrowhead=none, arrowtail=none];
    e->3[arrowhead=none, arrowtail=none];
    e->a1[arrowhead=none, arrowtail=none];
    e->a2[arrowhead=none, arrowtail=none];
    e->a3[arrowhead=none, arrowtail=none];
    f->1[arrowhead=none, arrowtail=none];
    f->4[arrowhead=none, arrowtail=none];
    f->7[arrowhead=none, arrowtail=none];
    f->a1[arrowhead=none, arrowtail=none];
    f->a4[arrowhead=none, arrowtail=none];
    f->a7[arrowhead=none, arrowtail=none];
    g->5[arrowhead=none, arrowtail=none];
    g->6[arrowhead=none, arrowtail=none];
    g->7[arrowhead=none, arrowtail=none];
    g->a5[arrowhead=none, arrowtail=none];
    g->a6[arrowhead=none, arrowtail=none];
    g->a7[arrowhead=none, arrowtail=none];
}