At first a graph is constructed

L=Graph[{1\[UndirectedEdge]2,1\[UndirectedEdge]3,2\[UndirectedEdge]3,2\[UndirectedEdge]4,2\[UndirectedEdge]6,3\[UndirectedEdge]5,3\[UndirectedEdge]7,4\[UndirectedEdge]6,5\[UndirectedEdge]7,6\[UndirectedEdge]7,6\[UndirectedEdge]8,7\[UndirectedEdge]8}]

{VertexList[L],EdgeList[L],VertexCount[L],EdgeCount[L]}

ConnectedComponents[Graph[{1\[UndirectedEdge]2,2\[UndirectedEdge]3,3\[UndirectedEdge]1,4\[UndirectedEdge]5},VertexLabels->"Name",ImagePadding->5]]

am=AdjacencyMatrix[L]

AdjacencyGraph[AdjacencyMatrix[L]]

FromAdjacencyMatrix and ToAdjacencyMatrix are not built in.

So far so good. Let us invoke the package.

<<Combinatorica`

A lot of functions, like Graph, ConnectedCompomnents will not function any more.

Graph[{1\[UndirectedEdge]2,1\[UndirectedEdge]3,2\[UndirectedEdge]3,2\[UndirectedEdge]4,2\[UndirectedEdge]6,3\[UndirectedEdge]5,3\[UndirectedEdge]7,4\[UndirectedEdge]6,5\[UndirectedEdge]7,6\[UndirectedEdge]7,6\[UndirectedEdge]8,7\[UndirectedEdge]8}]

ConnectedComponents[Graph[{1\[UndirectedEdge]2,2\[UndirectedEdge]3,3\[UndirectedEdge]1,4\[UndirectedEdge]5},VertexLabels->"Name",ImagePadding->5]]

ConnectedComponents[L]

HamiltonianQ is avaliable but it does not work

HamiltonianQ[L]

HamiltonianCycle[L]

AdjacencyGraph[am]

FromAdjacencyMatrix[am]

FromAdjacencyMatrix[nam=Normal[am]]

Use of sparse matrices are discouraged, they are incompatible with Combinatorica.

MatrixForm[am]

HamiltonianQ[AdjacencyGraph[am]]

HamiltonianQ[AdjacencyGraph[nam]]

HamiltonianQ[FromAdjacencyMatrix[nam]]

{V[L],M[L]}

{V[AdjacencyGraph[am]],M[AdjacencyGraph[am]]}

{V[AdjacencyGraph[nam]],M[AdjacencyGraph[nam]]}

{V[FromAdjacencyMatrix[nam]],M[FromAdjacencyMatrix[nam]]}