Not all nodes in the network are of equal importance. Centrality is a concept in graph theory that describes the importance of a node in a network. The most straightforward method of calculating the centrality of a node is to count the number of vertices (connections) that it has with other nodes. The example below shows a simple undirected graph and the degree of each node.

In a directed graph, like with Org-Roam, we can calculate the in-degree and out-degree, the number of vertices point to the node, or the number of vertices pointing from the node (the number of backlinks and the number of links). The degree() function of the iGraph package calculates degree centrality. The code below generates a table with the top ten most connected nodes.

## Centrality
centrality <- tibble(Node = names(degree(g)),
                     Degree = degree(g, mode = "total"),
                     Links = degree(g, mode = "out"),
                     Backlinks = degree(g, mode = "in")) 

centrality %>% 
  top_n(n = 10) %>% 
  arrange(desc(Degree))

While some nodes might be more connected than others, it would also be good to know which nodes are closest to each other. In other words, can we find clusters of nodes (communities) to find meta-structure in the network? A community is a sub-network with densely connected nodes, but less so with nodes outside the community. Expressed probabilistically, two random nodes are more likely to be associated when they form part of the same community than when they don't. Thus, community detection increases the parsimony of the network by identifying those groups of nodes that are most closely related to each other.

Using the example network, two communities can be visually distinguished: nodes 1–4 and nodes 5–7. Texts A, B and C belong to the first community, while texts C and D belong to the second community. Text C (nodes 2 and 5) spans the two communities of discourse. This solution is valid because each node has more connections to nodes within its own community than nodes outside it.

The examples' communities are easily detected visually, but community detection becomes more difficult as the network grows. Community detection is a mathematical process to cluster nodes into cohesive sub-networks.

Several algorithms for community detection have been developed based on a range of mathematical principles. However, the numerical validation of community structure has not yet been satisfactorily solved, and no agreed single method exists to assess the quality of communities. In my research into knowledge networks, the Spinglass algorithm provided the most interpretable results.

## Community-detection
c <- cluster_spinglass(g)

This algorithm results in a named vector that assigns a number of each community to each node. Making sense of community structure requires some human interpretation because the algorithm does not analyse the texts, only the connections between them. Please note that clustering algorithms are computationally intensive and can take a while.

We can assign a name to each community by using the node's name with the most backlinks within each community. The code below creates a table of the community memberships and joins it with the centrality table. The last part assigns a name to each community by selecting the node's name with the most backlinks, counts the number of members and arranges the table by community size.

communities <- tibble(Node = c$names,
                      Community = c$membership) %>% 
  left_join(centrality) %>% 
  group_by(Community) %>% 
  summarise(Name = Node[which.max(Backlinks)],
            Nodes = n()) %>% 
  arrange(desc(Nodes))

When a network is fairly large it might be more informative to visualise only a section. The code below determines the number of the relevant node. The V() function holds the properties of al vertices (the nodes) in the network. The make_ego_graph() subsets a network from a given node (ego) and the order. This function creates a list of networks as you can enter more than one node.

## Subnetwork
node <- which(names(V(g)) == "Topology")
g1 <- make_ego_graph(g, order= 2, nodes = node)
c1 <- cluster_walktrap(g1[[1]])
    
plot(g1[[1]], layout = layout.kamada.kawai,
     mark.border = NA,
     vertex.size = sqrt(degree(g1[[1]])) + 2,
     vertex.color = c1$membership,
     vertex.frame.color = NA,
     vertex.label.family = "Sanserif",
     vertex.label.color = "black",
     edge.arrow.size = .3)

The networkD3 package can create interactive graphs, as implemented in this code snippet. The first step converts the iGraph object to a D3 object. Then, the htmlwidgets package lets you save this object as an interactive HTML file.

The code below adds the number of backlinks to the node table. Then, it defines the legend using the community names described above.

## Interactive visualisation
library(networkD3)
library(htmlwidgets)

## Convert to object suitable for networkD3
d3 <- igraph_to_networkD3(g, group = communities$Name[membership(c)])
d3$nodes$backlinks <- degree(g, mode = "in")

## Create force directed network plot
p <- forceNetwork(Links = d3$links, Nodes = d3$nodes, 
             Source = "source", Target = "target", 
             NodeID = "name", Group = "group", 
             Nodesize = "backlinks",
             zoom = TRUE, legend = TRUE)
saveWidget(p, file=paste0( getwd(), "/org-roam.html"))