igraph (version 1.0.1)

# cluster_edge_betweenness: Community structure detection based on edge betweenness

## Description

Many networks consist of modules which are densely connected themselves but sparsely connected to other modules.

## Usage

```cluster_edge_betweenness(graph, weights = E(graph)\$weight, directed = TRUE,
edge.betweenness = TRUE, merges = TRUE, bridges = TRUE,
modularity = TRUE, membership = TRUE)```

## Arguments

graph

The graph to analyze.

weights

The edge weights. Supply `NULL` to omit edge weights. By default the ‘`weight`’ edge attribute is used, if it is present.

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, ie. 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 edge betweenness score of an edge measures the number of shortest paths through it, see `edge_betweenness` for details. The idea of the edge betweenness based community structure detection is that it is likely that edges connecting separate modules have high edge betweenness as all the shortest paths from one module to another must traverse through them. So if we gradually remove the edge with the highest edge betweenness score we will get a hierarchical map, a rooted tree, called a dendrogram of the graph. The leafs of the tree are the individual vertices and the root of the tree represents the whole graph.

`cluster_edge_betweenness` performs this algorithm by calculating the edge betweenness of the graph, removing the edge with the highest edge betweenness score, then recalculating edge betweenness of the edges and again removing the one with the highest score, etc.

`edge.betweeness.community` returns various information collected throught the run of the algorithm. See the return value down here.

## 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.

## Examples

```# NOT RUN {
g <- barabasi.game(100,m=2)
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
# }
```