Re: creating adjacency matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg36587] Re: creating adjacency matrices*From*: Tom Burton <tburton at brahea.com>*Date*: Fri, 13 Sep 2002 01:13:57 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello, On 9/11/02 10:43 AM, in article alnvl6$7pn$1 at smc.vnet.net, "Moliterno, Thomas" <TMoliter at gsm.uci.edu> wrote: > I need to create an adjacency matrix from my data, which is currently in > the form of a .txt file and is basically a two column incidence list. > For example: > > 1 A > 1 B > 2 B > 3 C > . . > . . > . . > m n Past the following notebook into Mathematica. Tom Burton Notebook[{ Cell[CellGroupData[{ Cell["Preparing an adjacency matrix", "Section"], Cell["\<\ This notebook was prepared with the default cell output \ format type set to TraditionalForm. Then the output cells were \ removed to saved space. I recommend that execute this entire notebook \ before editing it.\ \>", "Text"], Cell[CellGroupData[{ Cell["Introduction", "Subsection"], Cell["\<\ Given the list of pairs of actors and events, it appears \ that most of the work is in preparing the associated list of \ undirected edges. So if you want only an adjacency matrix, it is \ perhaps more trouble that it's worth to prepare the associated graph. \ But the graph is nice, so I am showing both methods. \ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["The structure of a graph", "Subsection"], Cell["\<\ We need to investigate the structure of a graph so we can \ make our own graph.\ \>", "Text"], Cell[BoxData[ \(<< DiscreteMath`Combinatorica`\)], "Input"], Cell["Start with the simplest graph:", "Text"], Cell[BoxData[ \(aa = CompleteGraph[2]\)], "Input"], Cell[BoxData[ \(InputForm[aa]\)], "Input"], Cell["\<\ It appears to be a list of undirected edges followed by a \ list of vertices, each element of which is wrapped in an extra pair \ of braces. Let's try it:\ \>", "Text"], Cell[BoxData[ \(bb = Graph[{{{1, 2}}}, {{{\(-1. \), 0}}, {{1. , 0}}}]\)], "Input"], Cell[BoxData[ \(ToAdjacencyMatrix[aa]\)], "Input"], Cell[BoxData[ \(ToAdjacencyMatrix[bb]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Example of a list of actor-event pairs", "Subsection"], Cell[BoxData[ \(data = {{1, "\<B\>"}, {4, "\<A\>"}, {3, "\<C\>"}, {1, "\<A\>"}, \ {1, "\<D\>"}, {3, "\<B\>"}, {2, "\<C\>"}, {2, "\<B\>"}}\)], "Input"], Cell["\<\ Get the number of actors, which will be the dimension of \ the matrix and the number of vertices in the graph.\ \>", "Text"], Cell[BoxData[ \(d = Max[data[\([All, 1]\)]]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Getting the list of edges", "Subsection"], Cell[TextData[{ "Given the list of actors and actions, this is most of the work. \ I'll do it in baby steps, as I would like to see were I new to ", StyleBox["Mathematica", FontSlant->"Italic"], ". It could be done more directly." }], "Text"], Cell["Put events first.", "Text"], Cell[BoxData[ \(data2 = Reverse /@ data\)], "Input"], Cell["Group by event, with increasing actors within each event.", \ "Text"], Cell[BoxData[ \(data3 = Sort[data2]\)], "Input"], Cell[BoxData[ \(data4 = Split[data3, First[#1] == First[#2] &]\)], "Input"], Cell["Remove isolated pairs.", "Text"], Cell[BoxData[ \(data5 = DeleteCases[data4, {{_, _}}]\)], "Input"], Cell["Drop the actions.", "Text"], Cell[BoxData[ \(data6 = data5\[LeftDoubleBracket]All, All, 2\[RightDoubleBracket]\)], "Input"], Cell["\<\ Edges are all subsets of connected vertices taken two at a \ time:\ \>", "Text"], Cell[BoxData[ \(data7 = \(KSubsets[#, \ 2] &\) /@ data6\)], "Input"], Cell["Collect edges into one list", "Text"], Cell[BoxData[ \(data8 = Flatten[data7, 1]\)], "Input"], Cell["and remove duplicates", "Text"], Cell[BoxData[ \(onedir = Union[data8]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Adjacency matrix via a list of edges using MapAt", \ "Subsection"], Cell["Convert to directed edges", "Text"], Cell[BoxData[ \(bothdir = Join[onedir, Reverse /@ onedir]\)], "Input"], Cell["\<\ and finally, construct the adjacency matrix, putting 1's \ into elements corresponding to directed edges:\ \>", "Text"], Cell[BoxData[ \(emptymat = Table[0, {d}, {d}]\)], "Input"], Cell[BoxData[ \(adjmat = MapAt[1 &, emptymat, bothdir]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Adjacency matric via ToAdjacencyMatrix", "Subsection"], Cell["Construct a set of vertices for display", "Text"], Cell[BoxData[ \(verts = Table[{Cos[2 \[Pi]\ j/d], Sin[2 \[Pi]\ j/d]}, {j, d}]\)], "Input"], Cell["\<\ Prepare graph, adding extra braces and making the \ coordinates of the vertices real numbers (this appears to be \ necessary)\ \>", "Text"], Cell[BoxData[ \(g = Graph[List /@ onedir, N[List /@ verts]]\)], "Input"], Cell["Check our handiwork:", "Text"], Cell[BoxData[ \(InputForm[g]\)], "Input"], Cell[BoxData[ \(\(ShowGraph[g];\)\)], "Input"], Cell[BoxData[ \(ToAdjacencyMatrix[g]\)], "Input"] }, Open ]] }, Open ]] }, FrontEndVersion->"4.2 for Macintosh", ScreenRectangle->{{43, 1152}, {0, 746}}, WindowSize->{565, 624}, WindowMargins->{{243, Automatic}, {48, Automatic}} ]

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