igraph (version 1.1.1)

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"))

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.

Value

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

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

# NOT RUN {
g <- make_ring(10)
g <- add_edges(g, c(1,2, 2,3, 1,3))
coreness(g) 		# small core triangle in a ring

# }