How to manage distance between nodes in graphviz?

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];
}

To add to @uncletall answer (and partially address @ingomueller.net question), it looks like the nodesep and ranksep have big factors in how the nodes will be separated:

http://www.graphviz.org/doc/info/attrs.html#d:nodesep

nodesep : double, default: 0.25, minimum: 0.02 In dot, nodesep specifies the minimum space between two adjacent nodes in the same rank, in inches.

For other layouts, nodesep affects the spacing between loops on a single node, or multiedges between a pair of nodes.

Valid for: Graphs.

http://martin-loetzsch.de/S-DOT/ranksep.html

The gives desired rank separation, in inches. This is the minimum vertical distance between the bottom of the nodes in one rank and the tops of nodes in the next.