Controlling Layout of Graphviz Graphs

Answer 1

Use "constraint=false".

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

In your graph:

FourthSTATE -> ThirdSTATE [label="No" constraint=false] ;

You'll get:

digraph {
    ERROR [label="Error"];
    FirstSTATE [label="Initial State" URL="\ref FirstSTATE"];
    FirstSTATE -> SecondSTATE;
    SecondSTATE [label="Second State" URL="\ref SecondSTATE"];
    SecondSTATE -> ThirdSTATE;
    ThirdSTATE [label="Third State" URL="\ref ThirdSTATE"];
    FourthSTATE [label="Fouth State?" shape="diamond"];
    ThirdSTATE -> FourthSTATE;
    FourthSTATE -> FifthSTATE [label="Yes" ];
    FourthSTATE -> ThirdSTATE [label="No" constraint=false] ;
    FifthSTATE [label="Fifth State" URL="\ref FifthSTATE"];
    SixthSTATE [label="Sixth State?" shape="diamond"];
    SixthSTATE -> ERROR [label="Yes" ];
    SixthSTATE -> SeventhSTATE [label="No"];
    FifthSTATE -> SixthSTATE;
    SeventhSTATE [label="Seventh State" URL="\ref SeventhSTATE"];
    SeventhSTATE -> EighthSTATE;
    EighthSTATE [label="Eighth State" URL="\ref EighthSTATE"];
    NinthSTATE [label="Ninth State?" shape="diamond"];
    NinthSTATE -> TenthSTATE [label="Yes" ];
    NinthSTATE -> EighthSTATE [label="No"];
    EighthSTATE -> NinthSTATE;
    TenthSTATE [label="Tenth State" URL="\ref TenthSTATE"];
    EleventhSTATE [label="Eleventh State?" shape="diamond"];
    EleventhSTATE -> ERROR [label="Yes" ];
    EleventhSTATE -> TwelfthSTATE [label="No" ];
    TenthSTATE -> EleventhSTATE;
    TwelfthSTATE [label="Twelfth State" URL="\ref TwelfthSTATE"];
}