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.

Asked By: sol

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Source

Answer 1

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 )

Answered By: EnricoGiampieri

Answer 2

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

Answered By: unutbu

Drawing a graph or a network from a distance matrix?

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