Add assortativity

[heliosdrm]

I would like LG to have a function to obtain the assortativity coefficient. I would be willing to contribute code myself to add that feature, if only for the "global" coefficients as defined in Newman's papers for directed and undirected graphs. So I would like to ask:

• Taking into account that there was a frustrated attempt to do this in Assortativity #275, is there any reason besides that tests failed why this was closed and never resumed - in other words, a reason to refrain from submitting a new PR?
• LG has a big file structure. Where would the code for assortativity belong in?
• Any recommendation for writing the tests. I was planning to make a test for undirected graphs using Callaway's grown graph model, whose assortativity coefficient is formulated in Newman (2002) and could be tested for different values of the δ parameter; and a test for directed graphs based on some of the examples with given values in Newman (2003). Is that right? And where should I write the code for such tests?

[sbromberger]

cc @jpfairbanks

Hi @heliosdrm - thanks. I think what might make sense is for you to review #275, and if you can reuse the code there, please do so.

As far as where it goes, I'm at a loss. I'm thinking that the coefficient might be more related to a centrality measure of some sort. Your thoughts on this? Otherwise, we could create a new assortivity.jl if there are other related assortivity functions you plan on creating.

Tests should be placed in tests/ with the same file structure/names as where the code goes. As long as you have representative tests that cover each line of code, we should be ok.

Hope this helps. Thanks again.

[heliosdrm]

Thanks for the suggestions. I think that, rather than a centrality measure, assortativity might be considered a "community measure", since it describes to what extent the graph vertices are clustered depending on some similarity measure.

This is my proposal: create an assortativity.jl file in Community, with an AssortativityAlgorithm abstract type that defines how assortativity should be calculated. At the moment, the only available algorithm would be the Pearson correlation coefficient between a given measure that will be used to compare the source and destination vertices of each edge. This could be something like:

struct PearsonCorrelation{Ts, Td} <: AssortativityAlgorithm
    src_measure::Ts
    dst_measure::Td
end

The calculation would be done by a function such as assortativity(g::AbstractGraph, alg::AssortativityAlgorithm). The default algorithm in undirected graphs would be PearsonCorrelation(excessdegree, excessdegree), and in directed graphs it would be PearsonCorrelation(excessoutdegree, excessindegree). Now, excessdegree, etc. would be internal functions based on degree, indegree and outdegree that discount one unit from the degree of connected vertices, as normally done in the calculation of assortativity.

[heliosdrm]

What branch should I use to make the PR? The interfaces of the various branches in the repo are very different.