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Show first rules of TreePlot[ ] "upside-down" ? Show empty set as branch?

Posted 9 years ago

I have a list containing lots of graphs as lists of rules. Here is one:

In[152]:= tpaths[[2, 2, 200, 2]]

Out[152]= {{{"ABT", "AEE", "AEP"}, {"AGN", "AIG", "AIV"}, {"AXP", 
    "AZO", "BBT"}, {"BCR", "BEN", "CB"}, {"CCL", "CI", 
    "CL"}, {"CMCSA", "CMS", "CNP"}, {"COH", "COL", "COST"}, {"CTAS", 
    "D", "DG"}, {"DHR", "DIS", "DRI"}, {"DTE", "DUK", "ED"}, {"EMC", 
    "EQR", "ETR"}, {"EXC", "GAS", "GD"}, {"GLW", "GPC", "GT"}, {"HAS",
     "HON", "HSY"}, {"HUM", "IFF", "INTU"}, {"IPG", "JPM", 
    "K"}, {"KMB", "KMI", "LH"}, {"LMT", "LUV", "MCD"}, {"MKC", "MRK", 
    "MTB"}, {"MU", "NI", "NOC"}, {"NTRS", "PAYX", "PBI"}, {"PCG", 
    "PEG", "PEP"}, {"PFG", "PG", "PLD"}, {"PNW", "QCOM", 
    "SEE"}, {"SHW", "SNA", "SPG"}, {"SRE", "STJ", "SYMC"}, {"SYY", 
    "TE", "TJX"}, {"TMK", "TROW", "TXT"}, {"UNH", "UTX", 
    "YUM"}} -> {{"AEE", "AGN", "AIV"}, {"AXP", "AZO", "BBT"}, {"BCR", 
    "BEN", "CB"}, {"CCL", "CI", "CL"}, {"CMCSA", "CNP", 
    "COH"}, {"COL", "COST", "CTAS"}, {"DG", "DHR", "DIS"}, {"DRI", 
    "DTE", "ED"}, {"EMC", "EXC", "GAS"}, {"GD", "GLW", "GPC"}, {"GT", 
    "HAS", "HON"}, {"HUM", "INTU", "JPM"}, {"KMI", "LMT", 
    "LUV"}, {"MCD", "MRK", "MTB"}, {"NI", "NTRS", "PBI"}, {"PEP", 
    "PFG", "PG"}, {"QCOM", "SEE", "SNA"}, {"SRE", "STJ", 
    "SYMC"}, {"SYY", "TMK", "TROW"}, {"TXT", "YUM", " "}}, {{"ABT", 
    "AEE", "AEP"}, {"AGN", "AIG", "AIV"}, {"AXP", "AZO", 
    "BBT"}, {"BCR", "BEN", "CB"}, {"CCL", "CI", "CL"}, {"CMCSA", 
    "CMS", "CNP"}, {"COH", "COL", "COST"}, {"CTAS", "D", 
    "DG"}, {"DHR", "DIS", "DRI"}, {"DTE", "DUK", "ED"}, {"EMC", "EQR",
     "ETR"}, {"EXC", "GAS", "GD"}, {"GLW", "GPC", "GT"}, {"HAS", 
    "HON", "HSY"}, {"HUM", "IFF", "INTU"}, {"IPG", "JPM", 
    "K"}, {"KMB", "KMI", "LH"}, {"LMT", "LUV", "MCD"}, {"MKC", "MRK", 
    "MTB"}, {"MU", "NI", "NOC"}, {"NTRS", "PAYX", "PBI"}, {"PCG", 
    "PEG", "PEP"}, {"PFG", "PG", "PLD"}, {"PNW", "QCOM", 
    "SEE"}, {"SHW", "SNA", "SPG"}, {"SRE", "STJ", "SYMC"}, {"SYY", 
    "TE", "TJX"}, {"TMK", "TROW", "TXT"}, {"UNH", "UTX", 
    "YUM"}} -> {{"ABT", "AEP", "AIG"}, {"CMS", "D", "DUK"}, {"EQR", 
    "ETR", "HSY"}, {"IFF", "IPG", "K"}, {"KMB", "LH", "MKC"}, {"MU", 
    "NOC", "PAYX"}, {"PCG", "PEG", "PLD"}, {"PNW", "SHW", 
    "SPG"}, {"TE", "TJX", "UNH"}, {"UTX", " ", " "}}, {{"AEE", "AGN", 
    "AIV"}, {"AXP", "AZO", "BBT"}, {"BCR", "BEN", "CB"}, {"CCL", "CI",
     "CL"}, {"CMCSA", "CNP", "COH"}, {"COL", "COST", "CTAS"}, {"DG", 
    "DHR", "DIS"}, {"DRI", "DTE", "ED"}, {"EMC", "EXC", "GAS"}, {"GD",
     "GLW", "GPC"}, {"GT", "HAS", "HON"}, {"HUM", "INTU", 
    "JPM"}, {"KMI", "LMT", "LUV"}, {"MCD", "MRK", "MTB"}, {"NI", 
    "NTRS", "PBI"}, {"PEP", "PFG", "PG"}, {"QCOM", "SEE", 
    "SNA"}, {"SRE", "STJ", "SYMC"}, {"SYY", "TMK", "TROW"}, {"TXT", 
    "YUM", " "}} -> {{"AGN", "AXP", "BBT"}, {"BCR", "CCL", 
    "CMCSA"}, {"CTAS", "DRI", "DTE"}, {"ED", "GD", "KMI"}, {"MCD", 
    "MRK", "QCOM"}, {"SEE", " ", " "}}, {{"AEE", "AGN", 
    "AIV"}, {"AXP", "AZO", "BBT"}, {"BCR", "BEN", "CB"}, {"CCL", "CI",
     "CL"}, {"CMCSA", "CNP", "COH"}, {"COL", "COST", "CTAS"}, {"DG", 
    "DHR", "DIS"}, {"DRI", "DTE", "ED"}, {"EMC", "EXC", "GAS"}, {"GD",
     "GLW", "GPC"}, {"GT", "HAS", "HON"}, {"HUM", "INTU", 
    "JPM"}, {"KMI", "LMT", "LUV"}, {"MCD", "MRK", "MTB"}, {"NI", 
    "NTRS", "PBI"}, {"PEP", "PFG", "PG"}, {"QCOM", "SEE", 
    "SNA"}, {"SRE", "STJ", "SYMC"}, {"SYY", "TMK", "TROW"}, {"TXT", 
    "YUM", " "}} -> {{"AEE", "AIV", "AZO"}, {"BEN", "CB", 
    "CI"}, {"CL", "CNP", "COH"}, {"COL", "COST", "DG"}, {"DHR", "DIS",
     "EMC"}, {"EXC", "GAS", "GLW"}, {"GPC", "GT", "HAS"}, {"HON", 
    "HUM", "INTU"}, {"JPM", "LMT", "LUV"}, {"MTB", "NI", 
    "NTRS"}, {"PBI", "PEP", "PFG"}, {"PG", "SNA", "SRE"}, {"STJ", 
    "SYMC", "SYY"}, {"TMK", "TROW", "TXT"}, {"YUM", " ", 
    " "}}, {{"ABT", "AEP", "AIG"}, {"CMS", "D", "DUK"}, {"EQR", "ETR",
     "HSY"}, {"IFF", "IPG", "K"}, {"KMB", "LH", "MKC"}, {"MU", "NOC", 
    "PAYX"}, {"PCG", "PEG", "PLD"}, {"PNW", "SHW", "SPG"}, {"TE", 
    "TJX", "UNH"}, {"UTX", " ", " "}} -> {{"CMS", "D", "DUK"}, {"MU", 
    " ", " "}}, {{"ABT", "AEP", "AIG"}, {"CMS", "D", "DUK"}, {"EQR", 
    "ETR", "HSY"}, {"IFF", "IPG", "K"}, {"KMB", "LH", "MKC"}, {"MU", 
    "NOC", "PAYX"}, {"PCG", "PEG", "PLD"}, {"PNW", "SHW", 
    "SPG"}, {"TE", "TJX", "UNH"}, {"UTX", " ", " "}} -> {{"ABT", 
    "AEP", "AIG"}, {"EQR", "ETR", "HSY"}, {"IFF", "IPG", "K"}, {"KMB",
     "LH", "MKC"}, {"NOC", "PAYX", "PCG"}, {"PEG", "PLD", 
    "PNW"}, {"SHW", "SPG", "TE"}, {"TJX", "UNH", "UTX"}}, {{"AGN", 
    "AXP", "BBT"}, {"BCR", "CCL", "CMCSA"}, {"CTAS", "DRI", 
    "DTE"}, {"ED", "GD", "KMI"}, {"MCD", "MRK", "QCOM"}, {"SEE", " ", 
    " "}} -> {{"BBT", "DTE", "MRK"}, {"SEE", " ", " "}}, {{"AGN", 
    "AXP", "BBT"}, {"BCR", "CCL", "CMCSA"}, {"CTAS", "DRI", 
    "DTE"}, {"ED", "GD", "KMI"}, {"MCD", "MRK", "QCOM"}, {"SEE", " ", 
    " "}} -> {{"AGN", "AXP", "BCR"}, {"CCL", "CMCSA", "CTAS"}, {"DRI",
     "ED", "GD"}, {"KMI", "MCD", "QCOM"}}, {{"AEE", "AIV", 
    "AZO"}, {"BEN", "CB", "CI"}, {"CL", "CNP", "COH"}, {"COL", "COST",
     "DG"}, {"DHR", "DIS", "EMC"}, {"EXC", "GAS", "GLW"}, {"GPC", 
    "GT", "HAS"}, {"HON", "HUM", "INTU"}, {"JPM", "LMT", 
    "LUV"}, {"MTB", "NI", "NTRS"}, {"PBI", "PEP", "PFG"}, {"PG", 
    "SNA", "SRE"}, {"STJ", "SYMC", "SYY"}, {"TMK", "TROW", 
    "TXT"}, {"YUM", " ", " "}} -> {{"AIV", "AZO", "CNP"}, {"DG", 
    "EXC", "GLW"}, {"GPC", "GT", "JPM"}, {"LMT", "LUV", "PFG"}, {"PG",
     "STJ", "SYMC"}, {"SYY", "TMK", " "}}, {{"AEE", "AIV", 
    "AZO"}, {"BEN", "CB", "CI"}, {"CL", "CNP", "COH"}, {"COL", "COST",
     "DG"}, {"DHR", "DIS", "EMC"}, {"EXC", "GAS", "GLW"}, {"GPC", 
    "GT", "HAS"}, {"HON", "HUM", "INTU"}, {"JPM", "LMT", 
    "LUV"}, {"MTB", "NI", "NTRS"}, {"PBI", "PEP", "PFG"}, {"PG", 
    "SNA", "SRE"}, {"STJ", "SYMC", "SYY"}, {"TMK", "TROW", 
    "TXT"}, {"YUM", " ", " "}} -> {{"AEE", "BEN", "CB"}, {"CI", "CL", 
    "COH"}, {"COL", "COST", "DHR"}, {"DIS", "EMC", "GAS"}, {"HAS", 
    "HON", "HUM"}, {"INTU", "MTB", "NI"}, {"NTRS", "PBI", 
    "PEP"}, {"SNA", "SRE", "TROW"}, {"TXT", "YUM", " "}}, {{"CMS", 
    "D", "DUK"}, {"MU", " ", " "}} -> {}, {{"CMS", "D", "DUK"}, {"MU",
     " ", " "}} -> {{"CMS", "D", "DUK"}, {"MU", " ", " "}}, {{"ABT", 
    "AEP", "AIG"}, {"EQR", "ETR", "HSY"}, {"IFF", "IPG", "K"}, {"KMB",
     "LH", "MKC"}, {"NOC", "PAYX", "PCG"}, {"PEG", "PLD", 
    "PNW"}, {"SHW", "SPG", "TE"}, {"TJX", "UNH", "UTX"}} -> {{"AEP", 
    "EQR", "HSY"}, {"K", "KMB", "PCG"}, {"PEG", "PLD", "SPG"}, {"TE", 
    "TJX", " "}}, {{"ABT", "AEP", "AIG"}, {"EQR", "ETR", 
    "HSY"}, {"IFF", "IPG", "K"}, {"KMB", "LH", "MKC"}, {"NOC", "PAYX",
     "PCG"}, {"PEG", "PLD", "PNW"}, {"SHW", "SPG", "TE"}, {"TJX", 
    "UNH", "UTX"}} -> {{"ABT", "AIG", "ETR"}, {"IFF", "IPG", 
    "LH"}, {"MKC", "NOC", "PAYX"}, {"PNW", "SHW", "UNH"}, {"UTX", " ",
     " "}}, {{"BBT", "DTE", "MRK"}, {"SEE", " ", " "}} -> {{"BBT", 
    "DTE", "SEE"}}, {{"BBT", "DTE", "MRK"}, {"SEE", " ", 
    " "}} -> {{"MRK", " ", " "}}, {{"AGN", "AXP", "BCR"}, {"CCL", 
    "CMCSA", "CTAS"}, {"DRI", "ED", "GD"}, {"KMI", "MCD", 
    "QCOM"}} -> {{"AGN", "AXP", "CCL"}, {"CMCSA", "CTAS", 
    "DRI"}, {"ED", "MCD", "QCOM"}}, {{"AGN", "AXP", "BCR"}, {"CCL", 
    "CMCSA", "CTAS"}, {"DRI", "ED", "GD"}, {"KMI", "MCD", 
    "QCOM"}} -> {{"BCR", "GD", "KMI"}}, {{"AIV", "AZO", "CNP"}, {"DG",
     "EXC", "GLW"}, {"GPC", "GT", "JPM"}, {"LMT", "LUV", 
    "PFG"}, {"PG", "STJ", "SYMC"}, {"SYY", "TMK", " "}} -> {{"AZO", 
    "CNP", "DG"}, {"EXC", "GPC", "GT"}, {"LMT", "LUV", "PFG"}, {"PG", 
    "SYY", "TMK"}}, {{"AIV", "AZO", "CNP"}, {"DG", "EXC", 
    "GLW"}, {"GPC", "GT", "JPM"}, {"LMT", "LUV", "PFG"}, {"PG", "STJ",
     "SYMC"}, {"SYY", "TMK", " "}} -> {{"AIV", "GLW", "JPM"}, {"STJ", 
    "SYMC", " "}}, {{"AEE", "BEN", "CB"}, {"CI", "CL", "COH"}, {"COL",
     "COST", "DHR"}, {"DIS", "EMC", "GAS"}, {"HAS", "HON", 
    "HUM"}, {"INTU", "MTB", "NI"}, {"NTRS", "PBI", "PEP"}, {"SNA", 
    "SRE", "TROW"}, {"TXT", "YUM", " "}} -> {{"AEE", "BEN", 
    "CB"}, {"CI", "CL", "COH"}, {"COL", "COST", "DHR"}, {"EMC", "GAS",
     "HAS"}, {"HON", "HUM", "INTU"}, {"MTB", "NI", "NTRS"}, {"PBI", 
    "PEP", "SNA"}, {"SRE", "TROW", "YUM"}}, {{"AEE", "BEN", 
    "CB"}, {"CI", "CL", "COH"}, {"COL", "COST", "DHR"}, {"DIS", "EMC",
     "GAS"}, {"HAS", "HON", "HUM"}, {"INTU", "MTB", "NI"}, {"NTRS", 
    "PBI", "PEP"}, {"SNA", "SRE", "TROW"}, {"TXT", "YUM", 
    " "}} -> {{"DIS", "TXT", " "}}, {} -> {}, {} -> {}, {{"CMS", "D", 
    "DUK"}, {"MU", " ", " "}} -> {{"CMS", "D", "DUK"}, {"MU", " ", 
    " "}}, {{"CMS", "D", "DUK"}, {"MU", " ", " "}} -> {}, {{"AEP", 
    "EQR", "HSY"}, {"K", "KMB", "PCG"}, {"PEG", "PLD", "SPG"}, {"TE", 
    "TJX", " "}} -> {{"AEP", "EQR", "HSY"}, {"K", "KMB", 
    "PCG"}, {"TE", " ", " "}}, {{"AEP", "EQR", "HSY"}, {"K", "KMB", 
    "PCG"}, {"PEG", "PLD", "SPG"}, {"TE", "TJX", " "}} -> {{"PEG", 
    "PLD", "SPG"}, {"TJX", " ", " "}}, {{"ABT", "AIG", "ETR"}, {"IFF",
     "IPG", "LH"}, {"MKC", "NOC", "PAYX"}, {"PNW", "SHW", 
    "UNH"}, {"UTX", " ", " "}} -> {{"AIG", "ETR", "IFF"}, {"IPG", 
    "MKC", "NOC"}, {"PAYX", "PNW", "SHW"}, {"UTX", " ", 
    " "}}, {{"ABT", "AIG", "ETR"}, {"IFF", "IPG", "LH"}, {"MKC", 
    "NOC", "PAYX"}, {"PNW", "SHW", "UNH"}, {"UTX", " ", 
    " "}} -> {{"ABT", "LH", "UNH"}}}

When I TreePlot it with:

TreePlot[tpaths[[2, 2, 200, 2]], Left, VertexLabeling -> True]

I get a TreePlot where the first rules are shown at the bottom although I expected to see them on the top. Is there any option to show it "upside-down" ? My second problem is when a member for a rule is the empty set {}, then TreePlot does not show it as a branch, instead of the non-empty part of the branch is shown as a reflexive relation, that is the line is curved back to itself. I would like to se it as a binary branch with the empty set as one part and the root of the branch as the other part.

POSTED BY: Janos Lobb

Gave you SelfLoopStyle -> None a try? Or one could try to fill the empty lists or even empty rules with some flavours of Invisible ... The "upside-down" problem seems not to appear, because the first rules (in tpath[[2,2,200,2]]) appear on the left (Mathematica 10.4.1.0).

POSTED BY: Udo Krause
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