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Connected components of a graph

Source: R/components.R, R/structural.properties.R
components.Rd

Calculate the maximal (weakly or strongly) connected components of a graph

Usage

component_distribution(graph, cumulative = FALSE, mul.size = FALSE, ...)

largest_component(graph, mode = c("weak", "strong"))

components(graph, mode = c("weak", "strong"))

is_connected(graph, mode = c("weak", "strong"))

count_components(graph, mode = c("weak", "strong"))

Arguments

graph

The graph to analyze.

cumulative

Logical, if TRUE the cumulative distirubution (relative frequency) is calculated.

mul.size

Logical. If TRUE the relative frequencies will be multiplied by the cluster sizes.

...

Additional attributes to pass to cluster, right now only mode makes sense.

mode

Character string, either “weak” or “strong”. For directed graphs “weak” implies weakly, “strong” strongly connected components to search. It is ignored for undirected graphs.

Value

For is_connected() a logical constant.

For components() a named list with three components:

membership

numeric vector giving the cluster id to which each vertex belongs.

csize

numeric vector giving the sizes of the clusters.

no

numeric constant, the number of clusters.

For count_components() an integer constant is returned.

For component_distribution() a numeric vector with the relative frequencies. The length of the vector is the size of the largest component plus one. Note that (for currently unknown reasons) the first element of the vector is the number of clusters of size zero, so this is always zero.

For largest_component() the largest connected component of the graph.

Details

is_connected() decides whether the graph is weakly or strongly connected. The null graph is considered disconnected.

components() finds the maximal (weakly or strongly) connected components of a graph.

count_components() does almost the same as components() but returns only the number of clusters found instead of returning the actual clusters.

component_distribution() creates a histogram for the maximal connected component sizes.

largest_component() returns the largest connected component of a graph. For directed graphs, optionally the largest weakly or strongly connected component. In case of a tie, the first component by vertex ID order is returned. Vertex IDs from the original graph are not retained in the returned graph.

The weakly connected components are found by a simple breadth-first search. The strongly connected components are implemented by two consecutive depth-first searches.

See also

decompose(), subcomponent(), groups()

Connected components articulation_points(), biconnected_components(), decompose(), is_biconnected()

Other structural.properties: bfs(), connect(), constraint(), coreness(), degree(), dfs(), distance_table(), edge_density(), feedback_arc_set(), girth(), is_acyclic(), is_dag(), is_matching(), k_shortest_paths(), knn(), reciprocity(), subcomponent(), subgraph(), topo_sort(), transitivity(), unfold_tree(), which_multiple(), which_mutual()

Author

Gabor Csardi csardi.gabor@gmail.com

igraph_is_connected().

Examples


g <- sample_gnp(20, 1 / 20)
clu <- components(g)
groups(clu)
#> $`1`
#> [1] 1
#> 
#> $`2`
#> [1]  2  5  6  8 15
#> 
#> $`3`
#> [1] 3
#> 
#> $`4`
#> [1]  4 19
#> 
#> $`5`
#> [1]  7 10 11 12 13 14 18 20
#> 
#> $`6`
#> [1] 9
#> 
#> $`7`
#> [1] 16
#> 
#> $`8`
#> [1] 17
#> 
largest_component(g)
#> IGRAPH 6c0dc1f U--- 8 7 -- Erdos-Renyi (gnp) graph
#> + attr: name (g/c), type (g/c), loops (g/l), p (g/n)
#> + edges from 6c0dc1f:
#> [1] 2--3 1--4 4--5 2--6 5--6 6--7 6--8