Visualization graph by centralities

Question

I computed betweenness centralities of nodes in python igraph and saved it in csv file. Now i want to visual it in python and igraph library or gephi ,by centralities.

How can i do it?

Answer 1

Here is an example:

from igraph import *
import numpy as np

g = Graph.Famous("Zachary")

gamma = 0.33
plot(g, 
     vertex_color=[round(x) for x in rescale(np.array(g.betweenness())**gamma, out_range=(0, 255))], 
     palette=GradientPalette('Midnight Blue', 'Light Pink'),
     vertex_size = 12,
     bbox = (300,300))

Explanation:

Vertex colours can be specified (among other ways) as integers, representing an index into a palette. Here, I used a gradient palette between two colours. The default number of elements in a palette is 256, thus we need to generate colour indices between 0..255. The betweenness values are transformed to these with the help of the rescale function.

Additionally, I used a power-law transformation on the betweenness values with exponent gamma to make a smoother transition from small values (most vertices) to huge values (a few vertices).

To change the vertex area based on betweenness, you could use

plot(g, 
     vertex_size = (1 + np.array(g.betweenness())**0.5) * 3,
     bbox = (300,300))

The exponent 0.5 ensured that it is areas rather than radii that are proportional to betweenness. Adding 1 to the values ensures a minimum vertex size.