# edge.betweenness.community

##### Community structure detection based on edge betweenness

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

- Keywords
- graphs

##### Usage

```
edge.betweenness.community (graph, directed = TRUE,
edge.betweenness = TRUE, merges = TRUE, bridges = TRUE,
labels = TRUE)
edge.betweenness.community.merges (graph, edges)
```

##### Arguments

- graph
- The graph to analyze.
- 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 agglomerat - bridges
- Logical constant, whether to return a list the edge removals which actually splitted a component of the graph.
- labels
- Logical constant, whether to contain the labels of the
vertices in the result. More precisely, if the graph has a vertex
attribute valled
name , it will be part of the result object. - edges
- Numeric vector, the ids of the edges to be removed from a graph, all edges should be present in the vector, their order specifies the order of removal.

##### 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.

`edge.betweenness.community`

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.

`edge.betweenness.community.merges`

gets a list of edges and by
gradually removes them from the graph it creates a merge matrix
similar to the one returned by `edge.betweenness.community`

.

##### Value

- A named list is returned by
`edge.betweenness.community`

, with the following components: removed.edges Numeric vector, the edges of the graph, in the order of their removal. edge.betweenness Numeric vector, the edge betweenness value of the removed edges, the order is the same as in `removed.edges`

.merges Matrix containing the merges (ie. divisions) the algorithm performed, see the `merges`

argument for the format.bridges Numeric vector, the steps (ie. edge removals) which resulted a split of a component in the graph. labels The `name`

argument of the vertices.- Note that some components may be missing or
`NULL`

if you do not request them, see the parameters.A numeric matrix is returned by

`edge.betweenness.community.merges`

. The matrix has two column and its format is the same as the`merges`

slot of the result of`edge.betweenness.community`

.

##### concept

- Edge betweenness
- Community structure

##### 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,
`walktrap.community`

, `fastgreedy.community`

,
`leading.eigenvector.community`

for other community
detection methods. `as.dendrogram`

in package `stats`

for creating an
R dendrogram object from the result of the clustering. See
`community.to.membership`

to create the actual communities
after a number of edges removed from the network.

##### Examples

```
g <- barabasi.game(100,m=2)
eb <- edge.betweenness.community(g)
g <- graph.full(10) %du% graph.full(10)
g <- add.edges(g, c(0,10))
eb <- edge.betweenness.community(g)
E(g) [ eb$removed.edges[1] ]
```

*Documentation reproduced from package igraph, version 0.5.3, License: GPL (>= 2)*