igraph (version 1.3.5)

coreness: 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"))

Value

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

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.

Author

Gabor Csardi

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

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