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[SOLVED] Help understanding Partition Density

Computing metrics, community detection and data handling

[SOLVED] Help understanding Partition Density

Postby smitalm » 25 Feb 2013 21:58


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:

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.
Partition density definition
Last edited by smitalm on 07 Mar 2013 11:45, edited 1 time in total.
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Re: Help understanding Partition Density

Postby eduramiba » 25 Feb 2013 23:23

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)

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Re: Help understanding Partition Density

Postby smitalm » 26 Feb 2013 13:58

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