RE: creating adjacency matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg36576] RE: [mg36561] creating adjacency matrices*From*: "DrBob" <drbob at bigfoot.com>*Date*: Fri, 13 Sep 2002 01:13:37 -0400 (EDT)*Reply-to*: <drbob at bigfoot.com>*Sender*: owner-wri-mathgroup at wolfram.com

I'll assume you have the information in a matrix like x: TableForm[x = {{1, A }, {1, B }, {2, B}, {3, D}, {4, D}, {5, C}}] First find the highest actor number (or use what you've input elsewhere): m = Last[Union[x[[All,1]]]] 5 Define the incidence function: f[x_, a_, b_] /; a == b := 0 f[x_, a_, b_] := If[{} ≠ Intersection[Cases[x, {a, y_} -> y], Cases[x, {b, y_} -> y]], 1, 0] Here's the incidence matrix: Array[f[x, #1, #2] &, {m, m}] {{0, 1, 0, 0, 0}, {1, 0, 0, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 1, 0, 0}, { 0, 0, 0, 0, 0}} Once you have the incidence function, the only reason to store the incidence matrix is to avoid computing over again the same answers, and that can be accomplished in other ways. If you won't have other x matrices, it's convenient to define f this way: f[a_, b_] /; a == b := f[a, b] = 0 f[a_, b_] /; a < b := f[a, b] = If[{} ≠ Intersection[Cases[x, {a, y_} -> y], Cases[x, {b, y_} -> y]], 1, 0] f[a_, b_] := f[b, a] Array[f, {m, m}] {{0, 1, 0, 0, 0}, {1, 0, 0, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 0, 0}} Whenever you would want the {j,k} element of the adjacency matrix, just use f[j,k] instead. Each pair is computed only once. In this version, I've taken advantage of the symmetry of the problem, too, to cut the work in half. Bobby Treat -----Original Message----- From: Moliterno, Thomas [mailto:TMoliter at gsm.uci.edu] To: mathgroup at smc.vnet.net Subject: [mg36576] [mg36561] creating adjacency matrices 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 Where 1 to m represent actors and A to n represent events. My goal is to have an (m x m) matrix where cell i,j equals 1 if two actors are incident to the same event (in the sample above, 1 and 2 are both incident to B) and 0 otherwise (w/ zeros on the diagonal). I'm new to Mathmatica, and so I'm on the steep part of the learning curve ... All I've been able to figure out so far is how to get my incidence list into the program using Import["filename.txt"]. But then what? How do I convert to the adjacency matrix? I've found the ToAdjacencyMatrix[] command in DiscreteMath`Combinatorica`, but I can't seem to get it to work ... Thanks to any and all in advance. Tom ********************************************** Thomas P. Moliterno Graduate School of Management University of California, Irvine tmoliter at uci.edu **********************************************