[SOLVED] Help understanding Partition Density

[smitalm]

Hello,

i am implementing Link Communities community detection algorithm for gephi. I have trouble understanding explanation of partition density described in the paper (http://arxiv.org/pdf/0903.3178.pdf).

Here is only the part defining partition density:
http://imgur.com/nOxy5dl

I cannot find the connection between definition of link density (equation 2) and definition of partition density (equation 3). Because of that, i dont understand why is partition density defined the way it is. And i especially dont see how is (equation 3) calculating average of (equation 2) - if there is average, i would expect number of partitions (c) to be below horizontal line (in the divisor)

I do have the partition density calculation (equation 3) implemented, but since i am not sure i understand it correctly, i cannot be 100% sure if i am calculating it correctly (i am not getting very satisfying partition density values that i would expect).

I didnt know where else whould i ask this, and i could not google any other (more clear) definition of partition density.

Anyone who can shed some light into it would be appreciated.

[eduramiba]

Hi,
I may be wrong since I am not specially good with math, but here's what I understand:

In equation 3, it says that it's computing a weighted average, defined by the fraction of links that each partition has.
So each partition link density is multiplied by m_c/M since m_c is number of links in partition and M is the total number of links.

Then the equation 3 is transformed into the final one in a few steps (see attached image)

Eduardo

[smitalm]

This is even better explanation that i hoped for. Thank you for your time I am ashamed i did not see it myself