coreness: K-core decomposition of graphs

In igraph: Network Analysis and Visualization

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 [e-mail]

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()

Other structural.properties: bfs(), component_distribution(), connect(), constraint(), degree(), dfs(), distance_table(), edge_density(), feedback_arc_set(), girth(), is_acyclic(), is_dag(), is_matching(), k_shortest_paths(), knn(), reciprocity(), subcomponent(), subgraph(), topo_sort(), transitivity(), unfold_tree(), which_multiple(), which_mutual()

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 Oct. 20, 2024, 1:06 a.m.