This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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Graph Components and Connectivity
A graph may not be fully connected. For instance, only about 25% of the web graph is estimated to be in the largest strongly connected component. Another 25% is estimated to be in the in-component and 25% in the out-component of the strongly connected core. The remaining 25% is made up of smaller isolated components. For social graphs, one is often interested in -core components that indicate groups of people that are connected in a limited way.
Connected Components
ConnectedComponents give groups of vertices that are strongly connected
KCoreComponents give groups of vertices that are connected to at least others
ConnectedGraphQ test whether a graph is connected
Vertex Components
VertexComponent give the component for a set of vertices
VertexOutComponent give the out-component for a set of vertices
VertexInComponent give the in-component for a set of vertices