k-core of each node

The coreness of a node is the largest k such that it belongs to a subgraph in which every node has at least k neighbours (Seidman 1983), computed in O(nodes + edges) by the algorithm of Batagelj and Zaversnik. The cores are nested: the (k + 1)-core lies inside the k-core (proof("ntcore")). Edges are taken as undirected, without weights. Graph rules as in ntdeg().

Usage

ntcore(from, to, nodes = NULL)

Arguments

from, to

Labels of the two ends of each edge: vectors of the same length (zero when nodes gives every node) with no missing values.

nodes

NULL, or every node's label once: the node order of the results and the way to include isolated nodes.

Value

A data frame: node, core.

References

Seidman, S. B. (1983). Network structure and minimum degree. Social Networks, 5(3), 269-287. doi:10.1016/0378-8733(83)90028-X

Batagelj, V. and Zaversnik, M. (2003). An O(m) algorithm for cores decomposition of networks. doi:10.48550/arXiv.cs/0310049

Examples

ntcore(c(1, 1, 1, 2, 2, 3, 4), c(2, 3, 4, 3, 4, 4, 5))
#>   node core
#> 1    1    3
#> 2    2    3
#> 3    3    3
#> 4    4    3
#> 5    5    1