Connected components of the k-core as vertex lists
KCoreComponents[g, k]
KCoreComponents[g, k, "In"]
KCoreComponents[g, k, "Out"]
KCoreComponents[{v -> w, …}, …]
Table[HighlightGraph[g, Subgraph[g, Join@@KCoreComponents[g, k]], GraphHighlightStyle -> "DehighlightHide", PlotLabel -> "k=" <> ToString[k]], {k, 1, 3}]
→ {HighlightGraph[g, Subgraph[g, Join[g, 1]], GraphHighlightStyle -> DehighlightHide, PlotLabel -> k=1], HighlightGraph[g, Subgraph[g, Join[g, 2]], GraphHighlightStyle -> DehighlightHide, PlotLabel -> k=2], HighlightGraph[g, Subgraph[g, Join[g, 3]], GraphHighlightStyle -> DehighlightHide, PlotLabel -> k=3]}