Drawing a graph or a network from a distance matrix?

Question

I'm trying to plot/sketch (matplotlib or other python library) a 2D network of a big distance matrix where distances would be the edges of the sketched network and the line and column its nodes.

DistMatrix = [       'a',   'b',     'c',    'd'], ['a',   0,      0.3,    0.4,    0.7], ['b',   0.3,    0,      0.9,    0.2], ['c',   0.4,    0.9,    0,      0.1], ['d',   0.7,    0.2,    0.1,    0] ] 

I'm searching to sketch/plot the 2d network from such (bigger: thousand of columns and lines) distance matrix: node 'a' is linked to node 'b' by an edge depth of 0.3, nodes 'c' and 'd' would be tied by an edge depth of 0.1. What are the tools/libraries I can used (distance matrix can be converted into numpy matrix) to get the sketch/graphical projection of such network? (pandas, matplotlib, igraph,...?) and some leads to do that quickly (I would not define my self Tkinter function to do that ;-) ) ? thanks for your incoming answers.

Answer 1

The graphviz program neato tries to respect edge lengths. doug shows a way to harness neato using networkx like this:

import networkx as nx import numpy as np import string  dt = [('len', float)] A = np.array([(0, 0.3, 0.4, 0.7),                (0.3, 0, 0.9, 0.2),                (0.4, 0.9, 0, 0.1),                (0.7, 0.2, 0.1, 0)                ])*10 A = A.view(dt)  G = nx.from_numpy_matrix(A) G = nx.relabel_nodes(G, dict(zip(range(len(G.nodes())),string.ascii_uppercase)))      G = nx.drawing.nx_agraph.to_agraph(G)  G.node_attr.update(color="red", style="filled") G.edge_attr.update(color="blue", width="2.0")  G.draw('/tmp/out.png', format='png', prog='neato') 

yields

---

If you want to generate a dot file, you can do so using

G.draw('/tmp/out.dot', format='dot', prog='neato') 

which yields

strict graph {     graph [bb="0,0,226.19,339.42"];     node [color=red,         label="\N",         style=filled     ];     edge [color=blue,         width=2.0     ];     B    [height=0.5,         pos="27,157.41",         width=0.75];     D    [height=0.5,         pos="69,303.6",         width=0.75];     B -- D   [len=2.0,         pos="32.15,175.34 40.211,203.4 55.721,257.38 63.808,285.53"];     A    [height=0.5,         pos="199.19,18",         width=0.75];     B -- A   [len=3.0,         pos="44.458,143.28 77.546,116.49 149.02,58.622 181.94,31.965"];     C    [height=0.5,         pos="140.12,321.42",         width=0.75];     B -- C   [len=9.0,         pos="38.469,174.04 60.15,205.48 106.92,273.28 128.62,304.75"];     D -- A   [len=7.0,         pos="76.948,286.17 100.19,235.18 167.86,86.729 191.18,35.571"];     D -- C   [len=1.0,         pos="94.274,309.94 100.82,311.58 107.88,313.34 114.45,314.99"];     A -- C   [len=4.0,         pos="195.67,36.072 185.17,90.039 154.1,249.6 143.62,303.45"]; } 

The png file could then be generated using the graphviz neato program:

neato -Tpng -o /tmp/out.png /tmp/out.dot  

Answer 2

You can use the networkx package, that work perfectly with this kind of problems. Adjust your matrix to remove a simple numpy array like this:

DistMatrix =array([[0,      0.3,    0.4,    0.7], [0.3,    0,      0.9,    0.2], [0.4,    0.9,    0,      0.1], [0.7,    0.2,    0.1,    0] ]) 

then import networkx and use it

import networkx as nx G = G=nx.from_numpy_matrix(DistMatrix) nx.draw(G) 

if you want to draw a weighted version of the graph, you have to specify the color of each edge (at least, I couldn't find a more automated way to do it):

nx.draw(G,edge_color = [ i[2]['weight'] for i in G.edges(data=True) ], edge_cmap=cm.winter )