Find the 3-core components of a graph:

Show the 3-core components:

Find the 4-core components in a social network:

KCoreComponents works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

KCoreComponents finds core components of any size:

Find k-core components with vertex in-degrees at least k:

Find k-core components with vertex out-degrees at least k:

Use rules to specify the graph:

KCoreComponents gives an empty list if there is no k-core:

KCoreComponents works with large graphs:

Highlight the k-cores of a graph:

Find the degeneracy of a graph g, being the largest k such that g has a k-core:

Trees and forests are 1-degenerate graphs:

The Barabasi–Albert model with k edges added at each step is k-degenerate:

A social network:

Group actors:

Highlight groups:

Find k-core components by repeatedly removing vertices of out-degree less than k:

First iteration:

Second iteration:

No more vertices are removed by further iteration:

Use ConnectedComponents to obtain the components of the k-core:

The obtained k-cores of undirected graphs are connected:

A vertex in a k-core component c_i has at least k neighbors in c_i:

For an undirected graph, the vertex in-degree and out-degree are equal to the vertex degree:

The k-core vertex in-degree and out-degree components are equal to the k-core components:

The maximum clique of size k+1 is contained in a k-core component:

A k-core component is contained in a (k-1)-core component:

The adjacency matrix of a k-core component has at least k nonzero entries in each row:

The adjacency matrix of a k-core in-degree component has at least k nonzero entries in each column:

The adjacency matrix of a k-core out-degree component has at least k nonzero entries in each row: