Modularity Score

[ticoalu]

I read both paper by Blondel et al (2008) and Lambiotte et al (2009) and somehow still have a difficulty understanding the meaning behind the score of "modularity" and "modularity with resolution". Would somebody kindly explain what these score means? Do they have something to do with the quality of the discovered communities, if so is lower or higher score is better?

If one is able to set the value of resolution to influence the number of communities and the size of the communities (lower resolution = more but smaller communities; higher resolution = less but larger communities), then how can one determine the optimum resolution considering both modularity scores?

Thank in advance!

[pegerp]

Hi ticoalu.

In practice higher modularity is better. The higher the value the better quality the partition is. Here's a visual example how the modularity affects the network partition: http://forum.gephi.org/viewtopic.php?t=1585. Also read Sebastien's (admin) reply to issue in the thread.

However the "resolution limit" of modularity optimization is exactly the dilemma that you are wondering. In large graphs the modularity optimization may yield high modularity - that is, a good partition of the network - but smaller communities are hidden inside the larger communities. By adjusting the resolution it is possible to find smaller communities but the value that the modularity algorithm is trying to optimize would become smaller and thus would seem worse.

Check out the Wikipedia page about it:
http://en.wikipedia.org/wiki/Modularity ... tion_limit.

Also I think Fig. 3 at http://www.pnas.org/content/104/1/36.full explains quite well the resolution problem of modularity optimization.

[ticoalu]

Pegerp,

Thank you so much for your insight! More things to read now.

[seinecle]

Hi,

I have recently attended a presentation by Vincent Traag (https://www.google.com/calendar/render? ... output=xml) where he warned against using modularity score to judge the quality of a partition. I left with the impression that modularity score was simply not to be used as a sign of a poor / good partition.

Best,

Clement

[vtraag]

Yes, indeed you can't use the raw modularity scores to say whether it is a "good" partition, because a similarly high score may also be obtained in a random graph. Compare it to the traditional clustering coefficient: if the two variables are independent (the 'null' condition), the correlation is zero, so any correlation away from zero is "high". For modularity however, this value is not zero for random graphs (the 'null' condition), so that it's difficult to say whether modularity is 'high' and therefore a 'good' partition.

One way to asses the significance of a partition (how different from the 'null' condition is it), would be the technique I introduced here (http://bit.ly/1aDFatJ).

There are by the way also ways to overcome the resolution limit (see http://bit.ly/1amD2Jj for technical details), but these are not implemented (yet) in Gephi. However, one would also need to choose a particular resolution value, for which it might helpt to construct a 'resolution profile': what do partitions look like for various resolutions (some details are provided in http://bit.ly/1aDFatJ).

Cheers,

Vincent

[admin]

Another approach is to extract community cores, see http://www.complexnetworks.fr/stable-co ... -networks/

[ticoalu]

Dear all,

I have not open the forum for a while, but I really appreciate your inputs! Thanks you very much.