# cluster_edge_betweenness

0th

Percentile

##### 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
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. 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, 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.

##### 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.

##### Value

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

##### References

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.

##### Aliases
• cluster_edge_betweenness
• edge.betweenness.community
##### Examples
# NOT RUN {
g <- sample_pa(100, m = 2, directed = FALSE)
eb <- cluster_edge_betweenness(g)

g <- make_full_graph(10) %du% make_full_graph(10)
eb <- cluster_edge_betweenness(g)
eb

# }

Documentation reproduced from package igraph, version 1.2.3, License: GPL (>= 2)

### Community examples

emmanuel.olemou@gmail.com at Apr 3, 2019 igraph v1.2.4

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

emmanuel.olemou@gmail.com at Apr 3, 2019 igraph v1.2.4

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