compare communities from graphs with different number of vertices

问题

I am calculating louvain communities on graphs of communications data, where vertices represent performers on a big project. The graphs represent different communication methods (e.g., email, phone).

We want to try to identify teams of performers from their communication data. Since performers have preferences for different communication methods, the graphs are of different sizes and may have some unique vertices which may not be present in both. When I try to compare the community objects from the respective graphs, igraph::compare() throws an exception. See toy reprex below.

I considered a dplyr::full_join() or inner_join() of the vertex lists before constructing the graph & community objects to make them the same size, but worry about the impact of doing so on the resulting cluster_louvain() solutions.

Any ideas on how I can compare the community objects to one another from these different communication methods? Thanks in advance!

library(tidyverse, warn.conflicts = FALSE)
library(igraph, warn.conflicts = FALSE)

nodes <- as_tibble(list(id = c("sample1", "sample2", "sample3")))
edge <- as_tibble(list(from = "sample1",
                       to = "sample2"))
net <- graph_from_data_frame(d = edge, vertices = nodes, directed = FALSE)
com <- cluster_louvain(net)

nodes2 <- as_tibble(list(id = c("sample1","sample21", "sample22","sample23"
                                )))
edge2 <- as_tibble(list(from = c("sample1", "sample21"),
                       to = c("sample21", "sample22")))
net2 <- graph_from_data_frame(d = edge2, vertices = nodes2, directed = FALSE)
com2 <- cluster_louvain(net2)

# # uncomment to see graph plots
# plot.igraph(net, mark.groups = com)
# plot.igraph(net2, mark.groups = com2)

compare(com, com2)
#> Error in i_compare(comm1, comm2, method): At community.c:3106 : community membership vectors have different lengths, Invalid value

^{Created on 2019-02-22 by the reprex package (v0.2.1)}

回答1:

You will not (I don't believe) be able to compare clustering algorithms from two different graphs that contain two different sets of nodes. Practically you can't do it in igraph and conceptually its hard because the way clustering algorithms are compared is by considering all pairs of nodes in a graph and checking whether they are placed in the same cluster or a different cluster in each of the two clustering approaches. If both clustering approaches typically put the same nodes together and the same nodes apart then they are considered more similar.¹

I suppose another valid way to approach the problem would be to evaluate how similar the clustering schemes are for purely the set of nodes that are the intersection of the two graphs. You'll have to decide what makes more sense in your setting. I'll show how to do it using the union of nodes rather than the intersection.

So you need all the same nodes in both graphs in order to make the comparison. In fact, I think the easier way to do it is to put all the same nodes in one graph and have different edge types. Then you can compute your clusters for each edge type separately and then make the comparison. The reprex below is hopefully clear:

# repeat your set-up
library(tidyverse, warn.conflicts = FALSE)
library(igraph, warn.conflicts = FALSE)

nodes <- as_tibble(list(id = c("sample1", "sample2", "sample3")))
edge <- as_tibble(list(from = "sample1",
                       to = "sample2"))

nodes2 <- as_tibble(list(id = c("sample1","sample21", "sample22","sample23")))
edge2 <- as_tibble(list(from = c("sample1", "sample21"),
                        to = c("sample21", "sample22")))

# approach from a single graph
# concatenate edges
edges <- rbind(edge, edge2)
# create an edge attribute indicating network type
edges$type <- c("phone", "email", "email")
# the set of nodes (across both graphs)
nodes <- unique(rbind(nodes, nodes2))

g <- graph_from_data_frame(d = edges, vertices = nodes, directed = F)

# We cluster over the graph without the email edges
com_phone <- cluster_louvain(g %>% delete_edges(E(g)[E(g)$type=="email"]))
plot(g, mark.groups = com_phone)

# Now we can cluster over the graph without the phone edges
com_email <- cluster_louvain(g %>% delete_edges(E(g)[E(g)$type=="phone"]))
plot(g, mark.groups = com_email)

# Now we can compare
compare(com_phone, com_email)
#> [1] 0.7803552

As you can see from the plots we pick out the same initial clustering structure you found in the separate graphs with the additions of the extra isolated nodes.

1: Obviously this is a pretty vague explanation. The default algorithm used in compare is from this paper, which has a nice discussion.

来源：https://stackoverflow.com/questions/54831407/compare-communities-from-graphs-with-different-number-of-vertices

标签

dplyr

igraph