# coreness: K-core decomposition of graphs In igraph: Network Analysis and Visualization

 coreness R Documentation

## K-core decomposition of graphs

### Description

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.

### Value

Numeric vector of integer numbers giving the coreness of each vertex.

### Author(s)

Gabor Csardi csardi.gabor@gmail.com

### 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.

`degree`

### Examples

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

```

igraph documentation built on Sept. 22, 2022, 9:07 a.m.