This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# KCoreComponents

 KCoreComponents gives the k-core components of the underlying simple graph of g. KCoreComponentsgives the k-core components with vertex in-degrees at least k. KCoreComponentsgives the k-core components with vertex out-degrees at least k.
• KCoreComponents returns a list of components , where each component is given as a list of vertices.
• A k-core component is a maximal weakly connected subgraph in which all vertices have degree at least k.
Find the 3-core components of a graph:
Find the k-cores of a graph:
Find the 2-core components of a directed graph:
In-degree components:
Out-degree components:
Find the 3-core components of a graph:
 Out[1]=

Find the k-cores of a graph:
 Out[2]=

Find the 2-core components of a directed graph:
 Out[2]=
In-degree components:
 Out[3]=
Out-degree components:
 Out[4]=
 Scope   (3)
KCoreComponents works with undirected graphs:
Directed graphs:
2-core components:
In-degree components:
Out-degree components:
Works with large graphs:
 Applications   (1)
Find the degeneracy of a graph g, being the largest k such that g has a k-core:
The obtained k-cores of undirected graphs are connected:
The k-core components can be found 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:
KCoreComponents gives the core components of the underlying simple graph:
New in 8