# Cannot get Mathematica to recognise Vertex Weights of Graph

I am using Mathematica Version 8.0

I've tried variations of the following commands, in order to assign the weight $1/k$ for vertex $k$, for a graph defined on {1,2,..,n} via the edge rule $$(k,k') \in E~~\textrm{if and only if}~~LCM(k,k')>n$$ My goal is to calculate the maximal independent set in this graph with respect to these vertex weights. There are no weights assigned at all. Here's the code I used.

f[n_, i_, j_] := If[ (LCM[i, j] <= n), 1, 0];

MM[n_] :=
Table[Table[1 - f[n, i, j], {i, n}], {j,n}];

MM20 := MM[20]; G := AdjacencyGraph[Table[x, {x, 20}], MM20];

Gw :=
Graph[G, VertexWeight -> Table[1/x, {x, 1, 20}]];


I have tried not including the list of vertices in the MM20 definition, including the weights, all in one go, to no avail. If I ask

PropertyValue[{Gw, 3}, VertexWeight]


of mathematica, it just echoes the command back with no output and a graphical representation of the graph.

I don't want to enter the edges and weights explicitly (as 1<-> 2, etc) since I want to run this for much bigger graphs. There must be something subtly wrong about how I am using the Table command, maybe?

Edit: Here's a screenshot of the problematic output

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• @MichaelE2 thanks, I have addressed the formatting issues, looks much better. Nov 9, 2015 at 0:16
• The PropertyValue expression you mention returns 1/3 when I execute it after evaluating the rest of your code. Is that not what you would like? (and thank you for formatting the question properly!) Nov 9, 2015 at 0:19
• @MarcoB, yes, that's what I would like, but what I was getting was PropertyValue[{Graph[plot, VertexWeight -> {1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/ 11, 1/12, 1/13, 1/14, 1/15, 1/16, 1/17, 1/18, 1/19, 1/20}], 3}, VertexWeight] ,so this is quite strange. I'll try again and see what happens, maybe in a new notebook. PS: I have said plot where a graphical rendering of the whole graph was output. Nov 9, 2015 at 0:29

Here's a slight refactoring of the OP's code, but the original code worked just as well. In particular I used Set (=) instead of SetDelayed (:=) for the graphs so they do not have to be recomputed each time they are used.

mm[n_] := SparseArray[{k_, kk_} /; LCM[k, kk] > n -> 1, {n, n}];


Note that the graph in the OP's screen shot is wrong. My guess is that G has been redefined, or failed to be defined. When I execute the OP's code, I get this for Gw, the same as my gw: