Eigenvector Centrallity Oddity with iGraph, Gephi, and NetworkX

I found something odd. 

I like graphs, and network analysis. I have have taken a few classes, and even written about the application of social network analysis to Enterprise Architecture (Data Structure Graphs). 

It my toolbox I use iGraph in R, NetworkX from Python, and Gephi for general analysis, visualization and network study. 

A segment of a social network (Photo credit: Wikipedia)

I stumbled onto something odd today. 

In R I loaded a graph originally generated from Gephi. Did a few calculations on the graph and converted the output to a data frame.

One of the metrics did not match between the two. 

Eigenvector Centrality. 

Thinking this only a little odd, I wrote some simple Python NetworkX code to assist me with determining which of the two answers was correct. 

Guess what? 

I got a third answer. 

I did some research on the mechanism used by each for calculating the Eigenvector Centrality measure. 

All of them appear to be valid. 

So, I created a test case. Using our friendly example of the konisberg bridges. The first image link in google that shows the bridges on today' google search is here: 

KonigsbergBridge

I created a simple input file to use in all three tools: 

Source	Target
A	C
A	B
B	A
B	C
B	D
D	B
D	C

Here are the results for Eigenvector Centrality using the tools mentioned above: 

Node Gephi iGraph NetworkX A 0.414195271 0.7379944 0.4351621 B 0.585804729 1 0.5573454 C 1 0.6814476 0.5573454 D 0.414195271 0.7379944 0.4351621

I realize that all of these tools use slightly different algorithms all written by different authors.

However, I would not expect the answers to quite so divergent for such a reference problem as the Konisberg bridges.


I wrote this to ask a few questions:

• Has anyone else noticed this? 
• Is there a set of options to pass to iGraph, Gephi, or NetworkX to make their calculations be similar? 
• What should be considered the proper Eigenvector centralities for the seven bridges of konisberg? 

I put all of my test code, along with test data on my github here: Eigenvector Questions

If anyone could point out a good way to get the same answer using multiple tools like this, I would appreciate it.


Thank you.