How are coordinates in plot(graph(M)) generated?

Given an undirected unweighted adjacency matrix M consisting of only ones and zeros, Matlab can generate a visual graph representation using:

p = plot(graph(M))

Depending on what the exact configuration of M is, the coordinates of p will be different. I have two questions:

1. What is the default method used by Matlab for generating coordinates in the plot p?
2. Are there alternatives to the default method, for example, if one would like to base location of nodes in the plot on some centrality measure of choice?

Answer 1

[Christine Tobler]

There are different layout methods for plotting a graph, which you can call as follows:

plot(graph(M), 'layout', LAY);

with LAY one of 'force', 'subspace', 'layered' and 'circle'. By default, one of the first three is chosen based on the structure and size of the input graph.

Alternative, you can compute the x- and y-coordinates of each node yourself, and use the command

plot(graph(M), 'XData', x, 'YData', y);

I'm not aware of methods to plot a graph based on a centrality measure. Do you have more information about this?

[Tobias Johansson]

Thank you for the response. I found the documentation a bit sparse in describing these methods (although 'circle' is straightforward of course). What does "based on structure and size of the graph" mean?

As for the second issue, sometimes I encounter graphs where the nodes are arranged in a circle, but nodes with higher degrees are closer to the centre of the circle. Here is one (free) program which does this and other centrality visualizations: http://socnetv.sourceforge.net/

A degree centrality graph for a scale-free network:

[Christine Tobler]

Currently, the choice between layouts is:

• 'subspace' for graphs with more than 100 nodes
• 'layered' for graphs with <= 100 nodes that have no cycles
• 'force' for graphs with <= 100 nodes that have cycles

For the second point, MATLAB does not provide such a layout method, but here is some code that generates something similar:

% Generate graph with few very central nodes:
M = sprandn(80, 80, 0.01);
M(1:5, :) = sprandn(5, 80, 0.3);
g = graph(M, 'upper');
h = plot(g);

% Layout plot based on degree-centrality:
d = degree(g);
r = max(d) + 2 - d;
phi = linspace(0, 360, numnodes(g)+1)';
phis = phi;
phis(end) = [];
h.XData = r.*cosd(phis);
h.YData = r.*sind(phis);
for ii=2:max(d)+2
  if any(r == ii)
    hold on;
    plot(ii*cosd(phi), ii*sind(phi), 'Color', [0.8 0.8 0.8]);
  end
end
uistack(h, 'top')

[Tobias Johansson]

Thank you very much.