# graph.coreness

From igraph v0.4.4
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

`graph.coreness(graph, mode="all")`

##### 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 i

##### 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 <- graph.ring(10)
g <- add.edges(g, c(0,1, 1,2, 0,2))
graph.coreness(g)
```

*Documentation reproduced from package igraph, version 0.4.4, License: GPL version 2 or later (June, 1991)*

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