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.