BUILT-IN MATHEMATICA SYMBOL

KCoreComponents

gives the k-core components of the underlying simple graph of g.

KCoreComponents

gives the k-core components with vertex in-degrees at least k.

KCoreComponents

gives the k-core components with vertex out-degrees at least k.

MORE INFORMATION

KCoreComponents works for any graph object.

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.

EXAMPLES

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Basic Examples (3)

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:

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Find the k-cores of a graph:

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Find the 2-core components of a directed graph:

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In-degree components:

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Out-degree components:

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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:

Properties & Relations (3)

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: