Calculate network density for thousands of small networks

Question

I have a text file with edge lists for many thousands of small undirected networks. Each network has roughly 500 to 5,000 edges. What I would like to do is calculate some basic network statistics for each (e.g., density, modularity, network diameter, etc.) I know how to calculate these statistics for one graph at a time, but I'm not sure how to approach doing so 20,000+ times.

Have any of you done something like this before? Below is an example of what my data look like. I start with a dataframe of three columns: Group, node1, node2. How would you, for example, use iGraph to calculate network density for each of these Groups?

example <- data.frame(Group = c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1),
                      node1 = c(29044437056,29044437056,29044437056,29044437056,29044437056,29044437056,29044437056,29044437056,29044437056,29044437056,29044437056,29044437056,29044437056,29044437056,29044448919,29044448919,29044448919,29044448919,29044448919,29044448919,29044448919,29044448919,29044448919,29244466839,29244466839,29244466839,29244466839,29244466839,29244466839,29244466839,29244466839,29244466839,29244466839,29244466839,29244466839,29244466839,29244466839,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244474341,29244477516,29244477516,29244477516,29244477516,29244477516,29244477516,29244477516,29244477516,29244477516,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,16344363817,20544470634,20544470634,20544470634,20544470634,20544470634,20544470634,20544470634,20544475593,20544475593,20544475593,20544475593,20544475593,20544475593,20544475593,27644433947,27644433947,27644433947,27644433947,27644433947,28044448304,28044448304,28044448304,28044448304,28044448304,28044448304,28044448304,28044448304,28044448304,28044448304,28044448304,28044448304,28044448304,28244449115,28244449115,28244449115,28244449115,28244449115,28244449115,28244449115,28244449115,28244449115,28244449115,28244449115,28244449115,28844475158,28844475158,28844475158,28844475158,28844475158,28844475158,28844475158,28844475158,28844475158,28844475158,27344453539,27344453539,27744602357,27744602357,27744602357,27744602357,27744602357,27744602357,27744602357,27744602357,27744602357,27744602357,27744602357,27744602357,27744602357,27744602357,27744602357,27744602357,27744602357,27844585852,27844585852,27844585852,27844585852,27844585852,27844585852,27844585852,27844585852,27844585852,27844585852,27844585852),
                      node2 = c(4150157,35132297,35802950,35822464,35971341,35977775,36724507,42658186,1342343023,13844310298,2942627924,2942653049,2942754180,7044274712,416815,1445929,4150157,33520419,33581908,34830906,35111568,43196961,1842681710,116621,1448848,1560392,3699562,29403184,34189928,35828823,36431606,37010998,37131488,42517640,345167839,11944262684,85006312408,618994,3430467,4150157,33829033,35535398,35760050,35893676,36026987,36163353,36322140,36330673,36431606,37153803,38448018,38674693,40028733,43210669,142215389,345171462,842325391,1242310442,1642273983,1842618408,1842735040,18444365571,18444368411,2342469450,2942529362,84942435207,33582733,34699937,34740905,35095498,37170843,37429426,37459916,1442276323,2542490252,336374,2373672,25785717,28377471,28381751,31275173,32210712,34774129,34831978,35264681,35339388,36192248,36270794,37189105,37470315,38547411,41702403,345753997,1142268042,12044251185,50749133132,57249093692,25785717,28091086,28825723,33622713,33991814,34621727,45449121012,336374,11187798,24280236,26239045,26516669,28091086,28783350,192917,1030529,32621080,42737988,1842779467,2853307,11760748,29359483,30681096,32620905,35156133,343831931,642306276,15844399352,15844415649,21544468072,21544480101,85010812746,1527454,27927261,30081829,30576834,32614970,32643182,35943888,37298440,39782265,2942653090,5544314341,85010812746,29150,1173576,32606366,36643771,37098560,37198509,37884702,42378607,242663463,3042545311,1344097,28204729,703370,781318,990010,1655009,30492538,32180421,34555959,34670902,35063206,35600561,35642940,37203284,37217019,37367130,14044260538,22044449563,4344598211,137774,213342,28199339,30218359,31276138,34129336,37062788,38121492,342666235,2542450463,9444241558))

Answer 1

groups = unique(example$Group)
densities = c()
for (i in 1:length(groups)) {
    graph = make_graph(as.character(c(t(as.matrix(example[which(example$Group == groups[i]),2:3])))), directed=F)
    densities = append(densities, graph.density(graph))
}


> data.frame(group = groups, density = densities)
  group    density
1     0 0.02563226
2     2 0.05714286
3     3 0.04429679
4     1 0.05681818

Answer 2

If you only need to compute the density, you dont necessarily need the igraph package. You could do this manually with:

library("dplyr")
example %>% 
  group_by(Group) %>%
  summarise( n = n_distinct( union(node1, node2)), obs = n(), density = obs/(n*(n-1)/2) ) %>%
  select(Group, density)

# A tibble: 4 x 2
  Group density
  <dbl>   <dbl>
1     0  0.0256
2     1  0.0568
3     2  0.0571
4     3  0.0443

If you also want to compute different network metrics, one option could be splitting the data, transform each of the splits into igraph objects and then apply a function that carries out the network analysis, as done here How can I calculate network measures separately for different periods using igraph in r?