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

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

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.

`cluster_edge_betweenness`

returns a
`communities`

object, please see the `communities`

manual page for 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.

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

`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.

# 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 # }