The k-core of graph is a maximal subgraph in which each vertex has at least degree k. The coreness of a vertex is k if it belongs to the k-core but not to the (k+1)-core.

## Usage

`coreness(graph, mode = c("all", "out", "in"))`

## Arguments

- graph
The input graph, it can be directed or undirected

- mode
The type of the core in directed graphs. Character constant, possible values:

`in`

: in-cores are computed,`out`

: out-cores are computed,`all`

: the corresponding undirected graph is considered. This argument is ignored for undirected graphs.

## Details

The k-core of a graph is the maximal subgraph in which every vertex has at least degree k. The cores of a graph form layers: the (k+1)-core is always a subgraph of the k-core.

This function calculates the coreness for each vertex.

## References

Vladimir Batagelj, Matjaz Zaversnik: An O(m) Algorithm for Cores Decomposition of Networks, 2002

Seidman S. B. (1983) Network structure and minimum degree, *Social
Networks*, 5, 269--287.

## See also

Other structural.properties:
`bfs()`

,
`component_distribution()`

,
`connect()`

,
`constraint()`

,
`degree()`

,
`dfs()`

,
`distance_table()`

,
`edge_density()`

,
`feedback_arc_set()`

,
`girth()`

,
`is_dag()`

,
`is_matching()`

,
`knn()`

,
`laplacian_matrix()`

,
`reciprocity()`

,
`subcomponent()`

,
`subgraph()`

,
`topo_sort()`

,
`transitivity()`

,
`unfold_tree()`

,
`which_multiple()`

,
`which_mutual()`

## Author

Gabor Csardi csardi.gabor@gmail.com