[Tex/LaTex] How to produce this Matlab social network graph from an adjacency matrix in Tikz

Question

I have a social network graph that I have made in Matlab using the graph object:

G = graph(weight);
LWidths = 10*G.Edges.Weight/max(G.Edges.Weight);
h = plot(G,'NodeLabel',cellstr(screen_names),'LineWidth',LWidths);
for i = 1:nnodes
    highlight(h,i, 'MarkerSize', counts(i))
end

where weight is an adjacency matrix, and counts is a vector with the node sizes. It looks something like this:

Now, I'm not happy with how this looks, so I want to make it with Tikz instead. So my question is: is it possible to produce this type of graph with Tikz from an adjacency matrix where the edges are of different width taken to be the nonzero elements of the matrix. The size of the nodes should also be different. I'm not very experienced in Tikz, so any guidance in how to proceed would be highly appreciated.

I have read this similar post, but I'm still not sure how to handle different edge widths and node sizes. Also, is it required to explicitly give the coordinates for the nodes or can they be automatically generated, as in Matlab?

Here is the weight matrix:

weight =

     0   741   630   406   325   325   351     0   300   276
   741     0   406   351   276     0     0     0     0     0
   630   406     0   300     0   276   300     0     0     0
   406   351   300     0     0     0     0     0     0     0
   325   276     0     0     0     0     0     0     0     0
   325     0   276     0     0     0   276     0     0     0
   351     0   300     0     0   276     0     0     0     0
     0     0     0     0     0     0     0     0     0     0
   300     0     0     0     0     0     0     0     0     0
   276     0     0     0     0     0     0     0     0     0

and counts vector:

counts = 

    56    42    39    34    32    31    30    29    28    28

Answer 1

A bit crude, but sort of works OK and requires lualatex. A simple parser (which just matches on non-whitespace) plus a graph drawing macro.

\RequirePackage{luatex85}
\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{graphs,graphdrawing}
\usegdlibrary{force,trees}
\usepackage{luacode}
\begin{luacode*}
function parseNetwork(nodeWeights, adjacencyMatrix)
  local i, j, n, v, w, str
  n = 0
  weights = {}
  for str in string.gmatch(nodeWeights, "[^%s]+") do
    w = tonumber(str)
        tex.print("n" .. n + 1 .. "/[minimum size=" .. w .. ", label=center:node" .. n  + 1 .. "];")
      n = n + 1
  end
  i = 0
  j = 0
  for str in string.gmatch(adjacencyMatrix, "[^%s]+") do
    v = tonumber(str)
      if v > 0 then
        if j > i then
        tex.print("n" .. i + 1 ..  " --[line width=" .. (v / 100) .. "]" .. "n" .. j + 1 .. ";")
        end
      end
        j = (j + 1) % n
        if j == 0 then i = i + 1 end
  end
end
\end{luacode*}
\tikzgraphsset{%
  node weights/.store in=\nodeweights,
  adjacency matrix/.store in=\adjacencymatrix,
  declare={network}{
  [/utils/exec={%
    \edef\networkspec{\directlua{parseNetwork("\nodeweights","\adjacencymatrix")}}},
    parse/.expanded=\networkspec] 
}}
\begin{document}
\begin{tikzpicture}
\graph [spring electrical layout, 
  edges={draw=blue!50!cyan, shorten >=-1em, shorten <=-1em}, 
  nodes={circle, fill=blue!50!cyan!50},
  electric charge=10]{
    network [
      node weights={
    56    42    39    34    32    31    30    29    28    28
    },
      adjacency matrix={
     0   741   630   406   325   325   351     0   300   276
   741     0   406   351   276     0     0     0     0     0
   630   406     0   300     0   276   300     0     0     0
   406   351   300     0     0     0     0     0     0     0
   325   276     0     0     0     0     0     0     0     0
   325     0   276     0     0     0   276     0     0     0
   351     0   300     0     0   276     0     0     0     0
     0     0     0     0     0     0     0     0     0     0
   300     0     0     0     0     0     0     0     0     0
   276     0     0     0     0     0     0     0     0     0
}]; 
};
\end{tikzpicture}
\end{document}