Network visualizations become common in science in practice. But as networks are increasing in size, common visualizations become less useful. There are simply too many node
I've been dealing with this problem recently. As a result, I've come up with another solution. Collapse the graph by communities/clusters. This approach is similar to the third option outlined by the OP above. As a word of warning, this approach will work best with undirected graphs. For example:
library(igraph)
set.seed(123)
g <- barabasi.game(1000) %>%
as.undirected()
#Choose your favorite algorithm to find communities. The algorithm below is great for large networks but only works with undirected graphs
c_g <- fastgreedy.community(g)
#Collapse the graph by communities. This insight is due to this post http://stackoverflow.com/questions/35000554/collapsing-graph-by-clusters-in-igraph/35000823#35000823
res_g <- simplify(contract(g, membership(c_g)))
The result of this process is the below figure, where the vertices' names represent community membership.
plot(g, margin = -.5)
The above is clearly nicer than this hideous mess
plot(r_g, margin = -.5)
To link communities to original vertices you will need something akin to the following
mem <- data.frame(vertices = 1:vcount(g), memeber = as.numeric(membership(c_g)))
IMO this is a nice approach for two reasons. First, it can in theory deal with any size graph. The process of finding communities can be continuously repeated on collapsed graphs. Second, adopting a interactive approach would yield very readable results. For example, one can imagine the user being able to click on a vertex in the collapsed graph to expand that community revealing all of its original vertices.