# coreness

From igraph v1.0.0
by Gabor Csardi

##### K-core decomposition of graphs

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.

- Keywords
- graphs

##### 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 fo

##### 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.

##### Value

- Numeric vector of integer numbers giving the coreness of 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

##### Examples

```
g <- make_ring(10)
g <- add_edges(g, c(1,2, 2,3, 1,3))
coreness(g) # small core triangle in a ring
```

*Documentation reproduced from package igraph, version 1.0.0, License: GPL (>= 2)*

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