I'm trying to create a graph with relationships of people involved in the 9/11 attacks, but I don't understand the input very much. I use loops to group the hijackers (hijacker1 knows hijacker2; hijacker5 knows hijacker3 etc.) but it doesn't work for me.
The result of my work should be a relationship graph as on this page: LINK
I use data in csv format: Data to download
The data schema looks like the screenshots below. There are three files available, but if I understand correctly to get what I want, enough data from the first file (?)
Hijackers ASSOCIATES
Hijackers ATTR
Hijackers PRIORITY_CONTACT
Hname1 HName2 HName3
HName1 0 1 0
HName2 1 0 1
HName3 0 1 0
...
I would like to draw a relationship diagram and extract information about which of the hijackers had the most relationships (Should I use betweenness() from igraph library?).
Here's an approach with igraph:
First, let's grab the data and make it into an adjacency matrix:
temp <- tempfile(fileext = ".zip")
download.file("https://sites.google.com/site/ucinetsoftware/datasets/covert-networks/911hijackers/9%2011%20Hijackers%20CSV.zip?attredirects=0&d=1",
temp,
mode = "wb")
data <- read.csv(unz(temp,"CSV/9_11_HIJACKERS_ASSOCIATES.csv"))
my.rownames <- data$X
data2 <- sapply(data[,-1], as.numeric)
rownames(data2) <- my.rownames
Adj <- as.matrix(data2)
Now the easy parts. We can convert the adjacency matrix into an igraph graph, compute vertex degree and add that data to to the graph.
library(igraph)
Graph <- graph_from_adjacency_matrix(Adj)
V(Graph)$vertex_degree <- degree(Graph)
Finally we can plot the graph with the vertex size being proportional to the degree:
plot.igraph(Graph,
vertex.size = V(Graph)$vertex_degree,
layout=layout.fruchterman.reingold, main="Hijacker Relationships")
Related
I'm in the process of creating a weighted igraph network object from a edge list containing two columns from and to. It has proven to be somewhat challenging for me, because when doing a workaround, I notice changes in the network metrics and I believe I'm doing something wrong.
library(igraph)
links <- read.csv2("edgelist.csv")
vertices <- read.csv2("vertices.csv")
network <- graph_from_data_frame(d=links,vertices = vertices,directed = TRUE)
##the following step is included to remove self-loops that I have used to include all isolate nodes to the network##
network <- simplify(network,remove.multiple = FALSE, remove.loops = TRUE)
In this situation I have successfully created a network object. However, it is not weighted. Therefore I create a second network object by taking the adjacency matrix from the objected created earlier and creating the new igraph object from it like this:
gettheweights <- get.adjacency(network)
network2 <- graph_from_adjacency_matrix(gettheweights,mode = "directed",weighted = TRUE)
However, after this when I call both of the objects, I notice a difference in the number of edges, why is this?
network2
IGRAPH ef31b3a DNW- 200 1092 --
network
IGRAPH 934d444 DN-- 200 3626 --
Additionally, I believe I've done something wrong because if they indeed would be the same network, shouldn't their densities be the same? Now it is not the case:
graph.density(network2)
[1] 0.02743719
graph.density(network)
[1] 0.09110553
I browsed and tried several different answers found from here but many were not 1:1 identical and I failed to find a solution.
All seems to be in order. When you re-project a network with edge-duplicates to be represented as a weight by the number of edges between given vertices, the density of your graph should change.
When you you test graph.density(network2) and graph.density(network), they should be different if indeed edge-duplicates were reduced to single-edges with weight as an edge attribute, as your output from network2 and network suggest.
This (over-) commented code goes through the process.
library(igraph)
# Data that should resemble yours
edges <- data.frame(from=c("A","B","C","D","E","A","A","A","B","C"),
to =c("A","C","D","A","B","B","B","C","B","D"))
vertices <- unique(unlist(edges))
# Building graphh in the same way as you do
g0 <- graph_from_data_frame(d=edges, vertices=vertices, directed = TRUE)
# Note that the graph is "DN--": directed, named, but NOT Weighted, since
# Instead of weighted edges, we have a whole lot of dubble edges
(g0)
plot(g0)
# We can se the dubble edges in the adjacency matrix as >1
get.adjacency(g0)
# Use simplify to remove LOOPS ONLY as we can see in the adjacency metrix test
g1 <- simplify(g0, remove.multiple = FALSE, remove.loops = TRUE)
get.adjacency(g1) == get.adjacency(g0)
# Turn the multiple edges into edge-weights by jumping through an adjacency matrix
g2 <- graph_from_adjacency_matrix(get.adjacency(g1), mode = "directed", weighted = TRUE)
# Instead of multiple edges (like many links between "A" and "B"), there are now
# just single edges with weights (hence the density of the network's changed).
graph.density(g1) == graph.density(g2)
# The former doubble edges are now here:
E(g2)$weight
# And we can see that the g2 is now "Named-Directed-Weighted" where g1 was only
# "Named-Directed" and no weights.
(g1);(g2)
# Let's plot the weights
E(g2)$width = E(g2)$weight*5
plot(g2)
A shortcoming of this/your method, however, is that the adjacency matrix is able to carry only the edge-count between any given vertices. If your edge-list contains more variables than i and j, the use of graph_from_data_frame() would normally embed edge-attributes of those variables for you straight from your csv-import (which is nice).
When you convert the edges into weights, however, you would loose that information. And, come to think of it, that information would have to be "converted" too. What would we do with two edges between the same vertices that have different edge-attributes?
At this point, the answer goes slightly beyond your question, but still stays in the realm of explaining the relation between graphs of multiple edges between the same vertices and their representation as weighted graphs with only one structural edge per verticy.
To convert edge-attributes along this transformation into a weighted graph, I suggest you'd use dplyr to "rebuild" any edge-attributes manually in order to keep control of how they are supposed to be merged down when recasting into a weighted one.
This picks up where the code above left off:
# Let's imagine that our original network had these two edge-attributes
E(g0)$coolness <- c(1,2,1,2,3,2,3,3,2,2)
E(g0)$hotness <- c(9,8,2,3,4,5,6,7,8,9)
# Plot the hotness
E(g0)$color <- colorRampPalette(c("green", "red"))(10)[E(g0)$hotness]
plot(g0)
# Note that the hotness between C and D are very different
# When we make your transformations for a weighted netowk, we loose the coolness
# and hotness information
g2 <- g0 %>% simplify(remove.multiple = FALSE, remove.loops = TRUE) %>%
get.adjacency() %>%
graph_from_adjacency_matrix(mode = "directed", weighted = TRUE)
g2$hotness # Naturally, the edge-attributes were lost!
# We can use dplyr to take controll over how we'd like the edge-attributes transfered
# when multiple edges in g0 with different edge attributes are supposed to merge into
# one single edge
library(dplyr)
recalculated_edge_attributes <-
data.frame(name = ends(g0, E(g0)) %>% as.data.frame() %>% unite("name", V1:V2, sep="->"),
hotness = E(g0)$hotness) %>%
group_by(name) %>%
summarise(mean_hotness = mean(hotness))
# We used a string-version of the names of connected verticies (like "A->B") to refere
# to the attributes of each edge. This can now be used to merge back the re-calculated
# edge-attributes onto the weighted graph in g2
g2_attributes <- data.frame(name = ends(g2, E(g2)) %>% as.data.frame() %>% unite("name", V1:V2, sep="->")) %>%
left_join(recalculated_edge_attributes, by="name")
# And manually re-attatch our mean-attributes onto the g2 network
E(g2)$mean_hotness <- g2_attributes$mean_hotness
E(g2)$color <- colorRampPalette(c("green", "red"))(max(E(g2)$mean_hotness))[E(g2)$mean_hotness]
# Note how the link between A and B has turned into the brown mean of the two previous
# green and red hotness-edges
plot(g2)
Sometimes, your analyses may benefit from either structure (weighted no duplicates or unweighted with duplicates). Algorithms for, for example, shortest paths are able to incorporate edge-weight as described in this answer, but other analyses might not allow for or be intuitive when using the weighted version of your network data.
Let purpose guide your structure.
I want to create a network graph of my data, where the weight of the edges is defined by the correlation coefficient in a correlation matrix. The connection is defined by being statistically significant or not.
Since I want to play around with some parameters I need to have this information in an edge list rather than in matrix form, but I'm struggling as to how to convert this. I have tried to used igraph as shown below, but I cannot figure out how to get the information on which correlations are significant and which are not into the edge list. I guess weight could be set to zero to code that info, but how do I combine a correlation matrix and a p-value matrix?
library(igraph)
g <- graph.adjacency(a,weighted=TRUE)
df <- get.data.frame(g)
df
It'd be great if you could provide a minimal reproducable example, but I think I understand what you're asking for. You'll need to make a graph from a matrix using graph_from_adjacency_matrix, but make sure to input something in the weighted parameter, because otherwise the elements in the matrix represent number of edges (less than 1 means no edges). Then you can create an edge list from the graph using as_data_frame. Then perform whatever calculation you want, or join any external data you have, then you can convert it back to a graph by using graph_from_data_frame
cor_mat <- cor(mtcars)
cor_g <- graph_from_adjacency_matrix(cor_mat, mode='undirected', weighted = 'correlation')
cor_edge_list <- as_data_frame(cor_g, 'edges')
only_sig <- cor_edge_list[abs(cor_edge_list$correlation) > .75, ]
new_g <- graph_from_data_frame(only_sig, F)
For the ones who still need this, here is the answer
library(igraph)
g <- graph.adjacency(a, mode="upper", weighted=TRUE, diag=FALSE)
e <- get.edgelist(g)
df <- as.data.frame(cbind(e,E(g)$weight))
I have a very large bipartite network model that I created from 5 million lines of a dataset. I decompose my network model because I can not draw a graph of this size. Now all I need is to plot the decompose graphics one by one. There is no problem with that. But I want to draw the graph with a shape according to the attributes of each node. For example, I want a square for the "A" attributes on my graph G, and a triangle for the "B" attributes. In addition to this I want to add vertex labels by attributes. Here is my codes to plot first component of graph after creating bipartite G and its work:
components <- decompose(G)
plot(components[[1]])
I tried something like this to adding labels and changing vertex shapes according to graph attributes but it didn't work:
plot(components[[1]], vertex.label= V(G)$attributes,
vertex.shape=c("square", "triangle"))
Does anyone can help me, I'm stuck. Thank you so much!
the components function returns a list of vertices which make up a component. So you need to traverse the list, create a subgraph and plot. As for plotting attributes you need to provide a reproducible example for us to help.
library(igraph)
set.seed(8675309)
g <- sample_gnp(200, p = 0.01)
V(g)$name <- paste0("Node", 1:vcount(g))
V(g)$shape <- sample(c("circle","square"), vcount(g), replace = T)
clu <- components(g)
grps <- groups(clu)
lapply(grps, function(x) plot(induced_subgraph(g, x)))
I have an interaction network and I used the following code to make an adjacency matrix and subsequently calculate the dissimilarity between the nodes of the network and then cluster them to form modules:
ADJ1=abs(adjacent-mat)^6
dissADJ1<-1-ADJ1
hierADJ<-hclust(as.dist(dissADJ1), method = "average")
Now I would like those modules to appear when I plot the igraph.
g<-simplify(graph_from_adjacency_matrix(adjacent-mat, weighted=T))
plot.igraph(g)
However the only thing that I have found thus far to translate hclust output to graph is as per the following tutorial: http://gastonsanchez.com/resources/2014/07/05/Pretty-tree-graph/
phylo_tree = as.phylo(hierADJ)
graph_edges = phylo_tree$edge
graph_net = graph.edgelist(graph_edges)
plot(graph_net)
which is useful for hierarchical lineage but rather I just want the nodes that closely interact to cluster as follows:
Can anyone recommend how to use a command such as components from igraph to get these clusters to show?
igraph provides a bunch of different layout algorithms which are used to place nodes in the plot.
A good one to start with for a weighted network like this is the force-directed layout (implemented by layout.fruchterman.reingold in igraph).
Below is a example of using the force-directed layout using some simple simulated data.
First, we create some mock data and clusters, along with some "noise" to make it more realistic:
library('dplyr')
library('igraph')
library('RColorBrewer')
set.seed(1)
# generate a couple clusters
nodes_per_cluster <- 30
n <- 10
nvals <- nodes_per_cluster * n
# cluster 1 (increasing)
cluster1 <- matrix(rep((1:n)/4, nodes_per_cluster) +
rnorm(nvals, sd=1),
nrow=nodes_per_cluster, byrow=TRUE)
# cluster 2 (decreasing)
cluster2 <- matrix(rep((n:1)/4, nodes_per_cluster) +
rnorm(nvals, sd=1),
nrow=nodes_per_cluster, byrow=TRUE)
# noise cluster
noise <- matrix(sample(1:2, nvals, replace=TRUE) +
rnorm(nvals, sd=1.5),
nrow=nodes_per_cluster, byrow=TRUE)
dat <- rbind(cluster1, cluster2, noise)
colnames(dat) <- paste0('n', 1:n)
rownames(dat) <- c(paste0('cluster1_', 1:nodes_per_cluster),
paste0('cluster2_', 1:nodes_per_cluster),
paste0('noise_', 1:nodes_per_cluster))
Next, we can use Pearson correlation to construct our adjacency matrix:
# create correlation matrix
cor_mat <- cor(t(dat))
# shift to [0,1] to separate positive and negative correlations
adj_mat <- (cor_mat + 1) / 2
# get rid of low correlations and self-loops
adj_mat <- adj_mat^3
adj_mat[adj_mat < 0.5] <- 0
diag(adj_mat) <- 0
Cluster the data using hclust and cutree:
# convert to dissimilarity matrix and cluster using hclust
dissim_mat <- 1 - adj_mat
dend <- dissim_mat %>%
as.dist %>%
hclust
clusters = cutree(dend, h=0.65)
# color the nodes
pal = colorRampPalette(brewer.pal(11,"Spectral"))(length(unique(clusters)))
node_colors <- pal[clusters]
Finally, create an igraph graph from the adjacency matrix and plot it using the fruchterman.reingold layout:
# create graph
g <- graph.adjacency(adj_mat, mode='undirected', weighted=TRUE)
# set node color and plot using a force-directed layout (fruchterman-reingold)
V(g)$color <- node_colors
coords_fr = layout.fruchterman.reingold(g, weights=E(g)$weight)
# igraph plot options
igraph.options(vertex.size=8, edge.width=0.75)
# plot network
plot(g, layout=coords_fr, vertex.color=V(g)$color)
In the above code, I generated two "clusters" of correlated rows, and a third group of "noise".
Hierarchical clustering (hclust + cuttree) is used to assign the data points to clusters, and they are colored based on cluster membership.
The result looks like this:
For some more examples of clustering and plotting graphs with igraph, checkout: http://michael.hahsler.net/SMU/LearnROnYourOwn/code/igraph.html
You haven't shared some toy data for us to play with and suggest improvements to code, but your question states that you are only interested in plotting your clusters distinctly - that is, graphical presentation.
Although igraph comes with some nice force directed layout algorithms, such as layout.fruchterman.reingold, layout_with_kk, etc., they can, in presence of a large number of nodes, quickly become difficult to interpret and make sense of at all.
Like this:
With these traditional methods of visualising networks,
the layout algorithms, rather than the data, determine the visualisation
similar networks may end up being visualised very differently
large number of nodes will make the visualisation difficult to interpret
Instead, I find Hive Plots to be better at displaying important network properties, which, in your instance, are the cluster and the edges.
In your case, you can:
Plot each cluster on a different straight line
order the placement of nodes intelligently, so that nodes with certain properties are placed at the very end or start of each straight line
Colour the edges to identify direction of edge
To achieve this you will need to:
use the ggnetwork package to turn your igraph object into a dataframe
map your clusters to the nodes present in this dataframe
generate coordinates for the straight lines and map these to each cluster
use ggplot to visualise
There is also a hiveR package in R, should you wish to use a packaged solution. You might also find another visualisation technique for graphs very useful: BioFabric
I am trying to figure out how to use graph.adjacency to create a graph using a correlation matrix (values -1 to 1), but only having the most strongly correlated edges included in the graph file, ie <-.8 or >.8
Here is the code that successfully gives me the network with the full data set:
corrdata<-read.csv("spearmancorr.csv",header=FALSE)
cor_mat<-as.matrix(corrdata)
diag(cor_mat)<-0
graph<-graph.adjacency(cor_mat,weighted=TRUE,mode="lower")
I tried using delete.edges to reduce the network to at least >.8 to test it out, but the resulting file still shows edge weights below 0.8
graph.copy <- delete.edges(graph, which(E(graph)$weight !<0.8)-1)
write.graph(graph.copy, file="gsig80.graphml", format="graphml")
Any advice on how to get the graph file I want?
You can delete the edges from the graph if you want to, or delete them from the matrix in the first place. E.g.
cor_mat[ cor_mat < .8 ] <- 0
diag(cor_mat) <- 0
graph <- graph.adjacency(cor_mat, weighted=TRUE, mode="lower")
Here is how to delete them from the graph, after creating it:
graph <- delete.edges(graph, E(graph)[ weight < 0.8 ])