How can I align nodes horizontally when rankdir=LR in graphviz - graphviz

Question

My code is
digraph{
rankdir=LR;
ratio=auto
node[shape=rectangle];
i0[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="2">
I<sub>0</sub>:
</TD>
<TD align="left">
S'→.bexpr<BR ALIGN="LEFT"/>
</TD>
</TR>
<TR>
<TD align="left" bgcolor="#aaaaaa">
bexpr→.bexpr or bterm <BR ALIGN="LEFT"/>
bexpr→.bterm <BR ALIGN="LEFT"/>
bterm→ .bterm and bfactor <BR ALIGN="LEFT"/>
bterm→.bfactor <BR ALIGN="LEFT"/>
bfactor→.not bfactor <BR ALIGN="LEFT"/>
bfactor→.(bexpr) <BR ALIGN="LEFT"/>
bfactor→.true <BR ALIGN="LEFT"/>
bfactor→.false <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i1[label=<
<TABLE border="0">
<TR>
<TD valign="top">
I<sub>1</sub>:
</TD>
<TD align="left">
S'→bexpr. <BR ALIGN="LEFT"/>
bexpr→bexpr .or bterm <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i2[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="1">
I<sub>2</sub>:
</TD>
<TD align="left">
bexpr→bterm. <BR ALIGN="LEFT"/>
bterm→bterm .and bfactor <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i3[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="1">
I<sub>3</sub>:
</TD>
<TD align="left">
bterm→bfactor.<BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i4[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="2">
I<sub>4</sub>:
</TD>
<TD align="left">
bfactor→not .bfactor <BR ALIGN="LEFT"/>
</TD>
</TR>
<TR>
<TD align="left" bgcolor="#aaaaaa">
bfactor→.not bfactor <BR ALIGN="LEFT"/>
bfactor→.(bexpr) <BR ALIGN="LEFT"/>
bfactor→.true <BR ALIGN="LEFT"/>
bfactor→.false <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i5[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="2">
I<sub>5</sub>:
</TD>
<TD align="left">
bfactor→(.bexpr) <BR ALIGN="LEFT"/>
</TD>
</TR>
<TR>
<TD align="left" bgcolor="#aaaaaa">
bexpr→.bexpr or bterm <BR ALIGN="LEFT"/>
bexpr→.bterm <BR ALIGN="LEFT"/>
bterm→.bterm and bfactor <BR ALIGN="LEFT"/>
bterm→.bfactor <BR ALIGN="LEFT"/>
bfactor→.not bfactor <BR ALIGN="LEFT"/>
bfactor→.(bexpr) <BR ALIGN="LEFT"/>
bfactor→.true <BR ALIGN="LEFT"/>
bfactor→.false <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i6[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="1">
I<sub>6</sub>:
</TD>
<TD align="left">
bfactor→true.<BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i7[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="1">
I<sub>7</sub>:
</TD>
<TD align="left">
bfactor→false. <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i8[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="2">
I<sub>8</sub>:
</TD>
<TD align="left">
bexpr→bexpr or .bterm <BR ALIGN="LEFT"/>
</TD>
</TR>
<TR>
<TD align="left" bgcolor="#aaaaaa">
bterm→ .bterm and bfactor <BR ALIGN="LEFT"/>
bterm→.bfactor <BR ALIGN="LEFT"/>
bfactor→.not bfactor <BR ALIGN="LEFT"/>
bfactor→.(bexpr) <BR ALIGN="LEFT"/>
bfactor→.true <BR ALIGN="LEFT"/>
bfactor→.false <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i9[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="2">
I<sub>9</sub>:
</TD>
<TD align="left">
bterm→ bterm and .bfactor <BR ALIGN="LEFT"/>
</TD>
</TR>
<TR>
<TD align="left" bgcolor="#aaaaaa">
bfactor→.not bfactor <BR ALIGN="LEFT"/>
bfactor→.(bexpr) <BR ALIGN="LEFT"/>
bfactor→.true <BR ALIGN="LEFT"/>
bfactor→.false <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i10[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="1">
I<sub>10</sub>:
</TD>
<TD align="left">
bfactor→not bfactor. <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i11[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="1">
I<sub>11</sub>:
</TD>
<TD align="left">
bfactor→(bexpr.) <BR ALIGN="LEFT"/>
bexpr→bexpr .or bterm <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i12[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="1">
I<sub>12</sub>:
</TD>
<TD align="left">
bexpr→bexpr or bterm. <BR ALIGN="LEFT"/>
bterm→ bterm .and bfactor <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i13[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="1">
I<sub>13</sub>:
</TD>
<TD align="left">
bterm→ bterm and bfactor. <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
i14[label=<
<TABLE border="0">
<TR>
<TD valign="top" rowspan="1">
I<sub>14</sub>:
</TD>
<TD align="left">
bfactor→(bexpr). <BR ALIGN="LEFT"/>
</TD>
</TR>
</TABLE>
>];
node[width=0.15,shape=none,fixedsize=false];
i2_1[label=<I<sub>2</sub>>];
i3_1[label=<I<sub>3</sub>>];
i3_2[label=<I<sub>3</sub>>];
i4_2[label=<I<sub>4</sub>>];
i4_3[label=<I<sub>4</sub>>];
i4_3[label=<I<sub>4</sub>>];
i5_1[label=<I<sub>5</sub>>];
i5_3[label=<I<sub>5</sub>>];
i5_4[label=<I<sub>5</sub>>];
i6_1[label=<I<sub>6</sub>>];
i6_2[label=<I<sub>6</sub>>];
i6_3[label=<I<sub>6</sub>>];
i6_4[label=<I<sub>6</sub>>];
i7_1[label=<I<sub>7</sub>>];
i7_2[label=<I<sub>7</sub>>];
i7_3[label=<I<sub>7</sub>>];
i7_4[label=<I<sub>7</sub>>];
i8_1[label=<I<sub>8</sub>>];
i9_1[label=<I<sub>9</sub>>];
i0 -> i1 [label ="bexpr"];
i0 -> i2 [label = "bterm"];
i0 -> i3 [label = "bfactor"];
i0 -> i4 [label = "not"];
i0 -> i5 [label = "("];
i0 -> i6 [label = "true"];
i0 -> i7 [label = "false"];
i1 -> i8 [label = "or"];
i2 -> i9 [label = "and"];
i4 -> i10 [label = "bfactor"];
i4 -> i4 [label = "not",weight=1];
i4 -> i5_1 [label = "("];
i4 -> i6_1 [label = "true"];
i4 -> i7_1 [label = "false"];
i5 -> i11 [label = "bexpr"];
i5 -> i2_1 [label ="bterm"];
i5 -> i3_1 [label = "bfactor"];
i5 -> i4_2 [label = "not"];
i5:sw -> i5:_ [label = "("];
i5 -> i6_2 [label = "true"];
i5 -> i7_2 [label = "false"];
i8 -> i12 [label = "bterm"];
i8 -> i3_2 [label = "bfactor"];
i8 -> i4_3 [label = "not"];
i8 -> i5_3 [label = "("];
i8 -> i6_3 [label = "true"];
i8 -> i7_3 [label = "false"];
i9 -> i13 [label = "bfactor"];
i9 -> i4_4 [label = "not"];
i9 -> i5_4 [label = "("];
i9 -> i6_4 [label = "true"];
i9 -> i7_4 [label = "false"];
i11 -> i14 [label = ")"];
i11 -> i8_1 [label = "or"];
i12 -> i9_1[label = "and"];
{rank = same;i0,i5};
}
And it generates this:
First, I want the I0, I1, I8, I12 to align horizontally. Does it have to use subgraph to wrap up some nodes? If it does, how? I have tried wrap I0, I1 nodes and the edge from I0 to I1 with a subgraph for a test. But that didn't make much change.
Secondly, can the self-loop in I5 look more elegant like the self-loop in I4 but not at the top of the node. I only find portpos option. If the node is a circle, the portpos option is enough. But it looks strange with rectangle.

Answer 1

Since no one answered, I asked the same question in the graphviz mailinglist and get the answer.
For the first question, add weight=100 to the edges. Here is what weight means from the manual:
Weight of edge. In dot, the heavier the weight, the shorter, straighter and more vertical the edge is.
For the second question, there is not perfect solution. An alteritive is leaving the control of edge to dot, but changing the position of label by option labelangle and labeldistance
i5 -> i5 [labelangle=20 labeldistance=2.5 taillabel = "("];
Thanks, Emden R. Gansner!

Answer 2

I can confirm that setting weight=100 worked to center the node in the cluster. I was searching for the settings in graphviz in order to center the units of the neural network I try to visualize. None of the attrs in the http://www.graphviz.org/doc/info/attrs.html looked obvious enough, but weight=100 on the edges certainly worked like a charm.