Lots of edges on a graph plot in python

Question

I have following script:

import pandas as pd
from igraph import *

df_p_c = pd.read_csv(\'data/edges.csv\')

...

edges = list_edges
vertices = list(dict_cas         


        

Answer 1

You seem to have a lot of small, disconnected components. If you want an informative graph, I think you should sort and group the connected components by size. Furthermore, the underlying assumption of many network layout algorithms is that there is a single giant component. Hence if you want sensible coordinates, you will often need to compute the layout for each component separately and then arrange the components with respect to each other. I would re-plot your graph in this way:

I have written the code for this graph using networkx as that is my module of choice. However, it would be very easy to substitute the networkx functions with igraph functions. The two functions that you need to replace are networkx.connected_component_subgraphs and whatever you want to use for the component_layout_func.

#!/usr/bin/env python

import numpy as np
import matplotlib.pyplot as plt
import networkx


def layout_many_components(graph,
                           component_layout_func=networkx.layout.spring_layout,
                           pad_x=1., pad_y=1.):
    """
    Arguments:
    ----------
    graph: networkx.Graph object
        The graph to plot.

    component_layout_func: function (default networkx.layout.spring_layout)
        Function used to layout individual components.
        You can parameterize the layout function by partially evaluating the
        function first. For example:

        from functools import partial
        my_layout_func = partial(networkx.layout.spring_layout, k=10.)
        pos = layout_many_components(graph, my_layout_func)

    pad_x, pad_y: float
        Padding between subgraphs in the x and y dimension.

    Returns:
    --------
    pos : dict node : (float x, float y)
        The layout of the graph.

    """

    components = _get_components_sorted_by_size(graph)
    component_sizes = [len(component) for component in components]
    bboxes = _get_component_bboxes(component_sizes, pad_x, pad_y)

    pos = dict()
    for component, bbox in zip(components, bboxes):
        component_pos = _layout_component(component, bbox, component_layout_func)
        pos.update(component_pos)

    return pos


def _get_components_sorted_by_size(g):
    subgraphs = list(networkx.connected_component_subgraphs(g))
    return sorted(subgraphs, key=len)


def _get_component_bboxes(component_sizes, pad_x=1., pad_y=1.):
    bboxes = []
    x, y = (0, 0)
    current_n = 1
    for n in component_sizes:
        width, height = _get_bbox_dimensions(n, power=0.8)

        if not n == current_n: # create a "new line"
            x = 0 # reset x
            y += height + pad_y # shift y up
            current_n = n

        bbox = x, y, width, height
        bboxes.append(bbox)
        x += width + pad_x # shift x down the line
    return bboxes


def _get_bbox_dimensions(n, power=0.5):
    # return (np.sqrt(n), np.sqrt(n))
    return (n**power, n**power)


def _layout_component(component, bbox, component_layout_func):
    pos = component_layout_func(component)
    rescaled_pos = _rescale_layout(pos, bbox)
    return rescaled_pos


def _rescale_layout(pos, bbox):

    min_x, min_y = np.min([v for v in pos.values()], axis=0)
    max_x, max_y = np.max([v for v in pos.values()], axis=0)

    if not min_x == max_x:
        delta_x = max_x - min_x
    else: # graph probably only has a single node
        delta_x = 1.

    if not min_y == max_y:
        delta_y = max_y - min_y
    else: # graph probably only has a single node
        delta_y = 1.

    new_min_x, new_min_y, new_delta_x, new_delta_y = bbox

    new_pos = dict()
    for node, (x, y) in pos.items():
        new_x = (x - min_x) / delta_x * new_delta_x + new_min_x
        new_y = (y - min_y) / delta_y * new_delta_y + new_min_y
        new_pos[node] = (new_x, new_y)

    return new_pos


def test():
    from itertools import combinations

    g = networkx.Graph()

    # add 100 unconnected nodes
    g.add_nodes_from(range(100))

    # add 50 2-node components
    g.add_edges_from([(ii, ii+1) for ii in range(100, 200, 2)])

    # add 33 3-node components
    for ii in range(200, 300, 3):
        g.add_edges_from([(ii, ii+1), (ii, ii+2), (ii+1, ii+2)])

    # add a couple of larger components
    n = 300
    for ii in np.random.randint(4, 30, size=10):
        g.add_edges_from(combinations(range(n, n+ii), 2))
        n += ii

    pos = layout_many_components(g, component_layout_func=networkx.layout.circular_layout)

    networkx.draw(g, pos, node_size=100)

    plt.show()


if __name__ == '__main__':

    test()

EDIT

If you want the subgraphs tightly arranged, you need to install rectangle-packer (pip install rectangle-packer), and substitute _get_component_bboxes with this version:

import rpack 

def _get_component_bboxes(component_sizes, pad_x=1., pad_y=1.):
    dimensions = [_get_bbox_dimensions(n, power=0.8) for n in component_sizes]
    # rpack only works on integers; sizes should be in descending order
    dimensions = [(int(width + pad_x), int(height + pad_y)) for (width, height) in dimensions[::-1]]
    origins = rpack.pack(dimensions)
    bboxes = [(x, y, width-pad_x, height-pad_y) for (x,y), (width, height) in zip(origins, dimensions)]
    return bboxes[::-1]

Answer 2

Do you know what meaning you are looking for? Or are you exploring? Or is this a specific question about zooming issues?

So far, you have done a good job of seeing the overall structure. Some ideas you might consider making new vocabulary with a few routines to support it. For example, if you make a small cluster be the set of points and edges that are together, then you can plot histograms, visualizations of clusters overlayed on each other, compare clusters with and without long nodes, and so one.

Answer 3

You could checkout networkx, which is a pretty nice graph library. Networkx has direct plotting support for matplotlib.

It supports various layout types, for example spring layout, random layout, and a few more

You should especially look at spring layout, which has a few interesting parameters for your use-case:

k (float (default=None)) – Optimal distance between nodes. If None the distance is set to 1/sqrt(n) where n is the number of nodes. Increase this value to move nodes farther apart.

Or both of these in combination with a custom layout:

pos (dict or None optional (default=None)) – Initial positions for nodes as a dictionary with node as keys and values as a coordinate list or tuple. If None, then use random initial positions.

fixed (list or None optional (default=None)) – Nodes to keep fixed at initial position.

The edge weight might also be something you can tune in order to get results you like:

weight (string or None optional (default=’weight’)) – The edge attribute that holds the numerical value used for the edge weight. If None, then all edge weights are 1.

I would recommend combining networkx with bokeh, which is a new plotting library that creates web-based html/js plots. It has direct support for networkx, and has some nice features like easy integration of node hover tools. If your graph isn't too big, the performance is pretty good. (I've plotted graphs with about 20000 nodes and a few thousand edges).

With both libraries combined, all you need is the following bit of code for a simple example (from the documentation) that tries to build an optimized layout:

import networkx as nx

from bokeh.io import show, output_file
from bokeh.plotting import figure
from bokeh.models.graphs import from_networkx

G=nx.karate_club_graph()  # Replace with your own graph

plot = figure(title="Networkx Integration Demonstration", x_range=(-1.1,1.1), y_range=(-1.1,1.1),
              tools="", toolbar_location=None)

graph = from_networkx(G, nx.spring_layout, scale=2, center=(0,0))
plot.renderers.append(graph)

output_file("networkx_graph.html")
show(plot)