How to draw bidirectional graph in Graphviz ordering levels by distance from some specified node (BFS order) - graphviz

Question

I have a graph in a form of an adjacency list. I want to draw it vertically and specify the root to be AA. I want to order the nodes in the levels by their BFS distance from the node AA (so in this case AA is on lavel 0 alone, JW HX MA KO are on level 1 etc...). How do I do that? Is there any automatic way? I don't want to specify levels manually by {rank=same; JW; HX; MA; KO;}...
The graph is below:
strict graph {
NV -- {ZV CG YB HX OY};
NU -- {DA MA OA DK};
VU -- {PS FX};
JW -- {AA MD};
RI -- {OY DG};
DG -- {TG RI DF EV KW};
PH -- {KW OW LT LZ};
KZ -- {ET QV CK MS};
IX -- {TS DO};
MS -- {LZ KZ};
IL -- {DO ET};
EJ -- {AV JY};
DK -- {NU CG};
YB -- {NV PS};
OA -- {YA NU};
DA -- {NU RG};
KO -- {AA TG};
RG -- {DF DA ZV MD LB};
MA -- {AA NU};
OW -- {DO PH};
KW -- {DG PH};
DO -- {IX IL CZ OW};
DF -- {RG DG};
TG -- {DG KO};
LB -- {RG FX};
HX -- {AA NV};
GB -- {AV XK};
CG -- {DK NV};
LT -- {AO PH};
FX -- {LB HY VU};
ET -- {IL KZ};
CK -- {UX KZ};
LZ -- {PH MS};
YA -- {JY OA};
TS -- {NO IX};
NO -- {TS};
XK -- {GB};
PS -- {EV VU YB};
AA -- {JW HX MA KO};
MD -- {JW RG};
JM -- {QV HY AO};
AV -- {EJ GB};
AO -- {JM LT};
JY -- {YA EJ};
OY -- {NV RI};
UX -- {CZ CK};
HY -- {JM FX};
EV -- {PS DG};
CZ -- {UX DO};
ZV -- {NV RG};
QV -- {JM KZ};
}

Answer 1

Unfortunately, dot on its own can't produce the graph you want. Dot's ranking algorithm is (almost) based on longest path instead of shortest path.
However, the Graphviz system also includes the dijkstra program (http://www.graphviz.org/pdf/dijkstra.1.pdf) that will annotate a graph with a distance attribute an a previous node attribute (along the shortest path) (Although the dijkstra algorithm differs from the BFS algorithm, I expect the results to be the same.)
As dot does not allow explicitly setting ranks (except for source and sink, some extra coding is needed to:
create subgraphs for the rank=same groupings
identify the "top" node - rank=source
set constraint=false on most edges (bidirectional graph causes dot to confuse ranks
set constraint=true on those edges that comprise shortest paths
The programming is done in gvpr (http://www.graphviz.org/pdf/gvpr.1.pdf), also included in the Graphviz package.
The gvpr program shortestPath.gvpr:
E{
$.constraint="false"; // default to false
}
BEG_G{
graph_t SG;
node_t aNode;
edge_t anEdge;
int D, oD, i, cnt;
float Df;
string tmpStr, pref="__addedSubg__";
string sameRank[], tok[int];
}
N{
if (hasAttr($, "dist") && $.dist!=""){
Df=(float)$.dist;
D=(int)Df; // convert to integer
$.Dist=D;
sameRank[D]=sprintf("%s %s", sameRank[D], $.name);
//print("// dist ", $.name, " ", $.dist, " ", D, " ", sameRank[D]);
if (hasAttr($, "prev") && $.prev!=""){
aNode=node($G, $.prev);
anEdge=edge(aNode, $, "");
// anEdge.constraint="true";
}
}
}
BEG_G{
}
N{
if (hasAttr($, "prev") && $.prev!=""){
aNode=node($G, $.prev);
if ($.Dist==aNode.Dist+1){
anEdge=edge(aNode, $, "");
anEdge.constraint="true";
}
}
}
END_G{
for (sameRank[D]){
print("// D SAME ", D, " ", sameRank[D]);
tmpStr=sprintf("%s%i", pref, D);
SG=subg($G, tmpStr);
if (D==0)
SG.rank="source";
else
SG.rank="same";
unset(tok);
cnt=tokens(sameRank[D], tok);
for (tok[i]){
aNode=node($G, tok[i]);
subnode(SG, aNode);
}
}
}
And a (Linux) command line of:
dijkstra -p AA autoRank0.gv|gvpr -c -f shortestPath.gvpr|dot -Tpng >oo.png
Giving: