Community structure detection based on edge betweenness

Community structure detection based on the betweenness of the edges in the network. This method is also known as the Girvan-Newman algorithm.

Usage

cluster_edge_betweenness(
  graph,
  weights = NULL,
  directed = TRUE,
  edge.betweenness = TRUE,
  merges = TRUE,
  bridges = TRUE,
  modularity = TRUE,
  membership = TRUE
)

Arguments

graph

The graph to analyze.

weights

The weights of the edges. It must be a positive numeric vector, NULL or NA. If it is NULL and the input graph has a ‘weight’ edge attribute, then that attribute will be used. If NULL and no such attribute is present, then the edges will have equal weights. Set this to NA if the graph was a ‘weight’ edge attribute, but you don't want to use it for community detection. Edge weights are used to calculate weighted edge betweenness. This means that edges are interpreted as distances, not as connection strengths.

directed

Logical constant, whether to calculate directed edge betweenness for directed graphs. It is ignored for undirected graphs.

edge.betweenness

Logical constant, whether to return the edge betweenness of the edges at the time of their removal.

merges

Logical constant, whether to return the merge matrix representing the hierarchical community structure of the network. This argument is called merges, even if the community structure algorithm itself is divisive and not agglomerative: it builds the tree from top to bottom. There is one line for each merge (i.e. split) in matrix, the first line is the first merge (last split). The communities are identified by integer number starting from one. Community ids smaller than or equal to \(N\), the number of vertices in the graph, belong to singleton communities, i.e. individual vertices. Before the first merge we have \(N\) communities numbered from one to \(N\). The first merge, the first line of the matrix creates community \(N+1\), the second merge creates community \(N+2\), etc.

bridges

Logical constant, whether to return a list the edge removals which actually splitted a component of the graph.

modularity

Logical constant, whether to calculate the maximum modularity score, considering all possibly community structures along the edge-betweenness based edge removals.

membership

Logical constant, whether to calculate the membership vector corresponding to the highest possible modularity score.

Value

cluster_edge_betweenness() returns a communities() object, please see the communities() manual page for details.

Details

The idea behind this method is that the betweenness of the edges connecting two communities is typically high, as many of the shortest paths between vertices in separate communities pass through them. The algorithm successively removes edges with the highest betweenness, recalculating betweenness values after each removal. This way eventually the network splits into two components, then one of these components splits again, and so on, until all edges are removed. The resulting hierarhical partitioning of the vertices can be encoded as a dendrogram.

cluster_edge_betweenness() returns various information collected through the run of the algorithm. Specifically, removed.edges contains the edge IDs in order of the edges' removal; edge.betweenness contains the betweenness of each of these at the time of their removal; and bridges contains the IDs of edges whose removal caused a split.

References

M Newman and M Girvan: Finding and evaluating community structure in networks, Physical Review E 69, 026113 (2004)

See also

edge_betweenness() for the definition and calculation of the edge betweenness, cluster_walktrap(), cluster_fast_greedy(), cluster_leading_eigen() for other community detection methods.

See communities() for extracting the results of the community detection.

Community detection as_membership(), cluster_fast_greedy(), cluster_fluid_communities(), cluster_infomap(), cluster_label_prop(), cluster_leading_eigen(), cluster_leiden(), cluster_louvain(), cluster_optimal(), cluster_spinglass(), cluster_walktrap(), compare(), groups(), make_clusters(), membership(), modularity.igraph(), plot_dendrogram(), split_join_distance(), voronoi_cells()

Author

Gabor Csardi csardi.gabor@gmail.com

Examples

g <- sample_pa(100, m = 2, directed = FALSE)
eb <- cluster_edge_betweenness(g)

g <- make_full_graph(10) %du% make_full_graph(10)
g <- add_edges(g, c(1, 11))
eb <- cluster_edge_betweenness(g)
eb
#> IGRAPH clustering edge betweenness, groups: 2, mod: 0.49
#> + groups:
#>   $`1`
#>    [1]  1  2  3  4  5  6  7  8  9 10
#>   
#>   $`2`
#>    [1] 11 12 13 14 15 16 17 18 19 20
#>