I've defined the function, drawGraph, to display a graph as follows:
drawGraph[g_] := GraphPlot[g, VertexLabeling -> True, DirectedEdges -> True]
If I specify a graph via its edges, and then ask for a hamiltonian cycle, everything works fine as seen below
However if I specify a graph via its adjacency matrix, and then ask for a hamiltonian cycle, I'm told that the adjacency matrix is not a graph. However I can display the adjacency matrix as a graph using my drawGraph function as seen below.
Why does the drawGraph function interpret the adjacency matrix as a graph but not the FindHamiltonianCycle function? The same problem exists with all the other Path functions -- ShortestPath, EulerianPath, etc.