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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.

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  • 1
    In theory, this could be impossible for certain distance matrices. Imagine e.g. a 4 x 4 distance matrix with all entries 1. This defines a three-dimensional simplex. There is no way to embed this graph into two dimensions isometrically. What should the program do in that case? Commented Nov 22, 2012 at 13:18
  • right, so no "edge length" but "edge depth that links two nodes Commented Nov 22, 2012 at 13:24

3 Answers 3

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35

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

enter image description here

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
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6 Comments

I have tried the code you suggest, adapted to my needs (remove the A.view) and it hasn't worked even for just 7 nodes. G is correct. What could have gone wrong? I am using graphviz 2.36.
This cases me error 'module' object has no attribute 'to_agraph'. To fix I used stackoverflow.com/questions/35279733/… and instead used nx.drawing.nx_agraph.to_agraph
How to draw the same graph in pure graphviz without python?
@Snochacz: I updated the answer to include the dot file generated by networkx.
I cannot install pygraphviz. Is it to possible to use neato and write the same algorithm with graphviz package (using pydot) ?
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22

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 )
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6 Comments

What is cm.winter?
@Sepide cm is from matplotlib and winter is a color map. matplotlib.org/stable/tutorials/colors/colormaps.html
how do we represent a missing edge? when there is no edge?
How to add the names on the points?
@MohamedHachaichi, nx.draw(G, with_labels=True) should do it.
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1

I had the same problem with you, so I made a Python package springpy to draw a graph from a distance matrix. Instead of using networkx and lots of code, springpy can create a graph in the simplest way possible.

Check this out:

import springpy as sp
matrix = [[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]]
sp.graph(matrix)

Moreover, it can even animate the process of caculation, by just the following code:

# Init matrix as above
sp.animate(matrix)

More infomation click here.

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