Assortativity

Hi,

As promised, here are the functions I wrote to compute the assortativity of graphs. I orientated myself on the respective functions in the igraph package (https://github.com/igraph/igraph/blob/master/src/mixing.c) and also used them as a benchmark. In the link you also find the references for the methods. A function to compute node-level assortativity will follow, hopefully in the course of today. The vertex categories/values have to supplied in the form of dictionaries.

###nominal assortativity
function assortativity_nominal(g,cat)
uc  = unique(values(cat))
nue = ne(g)
ai  = Dict()
bi  = Dict()
eii = Dict()
sumaibi = 0
sumeii  = 0

for (u,v) in edges(g)
ai[cat[u]]  = get(ai,cat[u],0) + 1
bi[cat[v]]  = get(bi,cat[v],0) + 1
cat[u] != cat[v] && continue
eii[cat[u]] = get(eii,cat[u],0) + 1
end

for c in uc
sumaibi += (ai[c]/nue) * (bi[c]/nue);
sumeii  += try (eii[c]/nue) catch 0 end;
end

if typeof(g)==LightGraphs.Graph
  sumaibi /= 4.0;
  sumeii  /= 2.0;
end

res = (sumeii - sumaibi) / (1.0 - sumaibi);

return res
end

###degree assortativity
function assortativity_degree(g)
nue  = ne(g)
sjk = 0
sj  = 0
sk  = 0
sjs = 0
sks = 0

for (u,v) in edges(g)
j   = outdegree(g,u) - 1;
k   = indegree(g,v)  - 1;
sjk += j*k
sj  += j
sk  += k
sjs += j^2
sks += k^2
end

if typeof(g)==LightGraphs.DiGraph
res = (sjk - sj*sk/nue)/sqrt((sjs - sj^2/nue)*(sks - sk^2/nue))
end

if typeof(g)==LightGraphs.Graph
res = (sjk/nue - ((sj + sk)/(2*nue))^2)/((sjs + sks)/(2*nue) - ((sj + sk)/(2*nue))^2)
end

return res
end

###assortativity
function assortativity(g, cat1, cat2 = "foo")
nue  = ne(g)
sjk = 0
sj  = 0
sk  = 0
sjs = 0
sks = 0

if cat2 == "foo"
cat2 = cat1
end

for (u,v) in edges(g)
j   = cat1[u];
k   = cat2[v];
sjk += j*k
sj  += j
sk  += k
sjs += j^2
sks += k^2
end

if typeof(g)==LightGraphs.DiGraph
res = (sjk - sj*sk/nue)/sqrt((sjs - sj^2/nue)*(sks - sk^2/nue))
end

if typeof(g)==LightGraphs.Graph
res = (sjk/nue - ((sj + sk)/(2*nue))^2)/((sjs + sks)/(2*nue) - ((sj + sk)/(2*nue))^2)
end

return res
end

[CarloLucibello]

Hi, nice work!

Can you add some tests, docs and file a Pull Request? This should be quick to review and merge

Also if this is a port from igraph this should be acknowledged with something like

# Ported from igraph library 
# https://github.com/igraph/igraph/blob/master/src/mixing.c

[sbromberger]

A PR would be nice - there are a few coding style things I'd recommend but it's hard to comment on a comment.

Hi, Sorry for my late reply. I made a pull request, with code including the local assortativity I was talking about above. I hope I did it correctly, I have not really used github before. Let me know if I have to change something.

[sbromberger]

Thanks. Let's move discussion over to #275.