It's slightly subtle (and confusing, I admit).
GraphPlot creates a
Graphics version of the
Graph. Hence the Head of your
GraphPlot is
Graphics and the error message from
ConnectedComponents is complaining about this. The argument of
ConnectedComponents must havve the Head
Graph. To get this you need to create your graph using the
Graph function as in (I've simplified your first argument just for my ease of reading):
g = Graph[{1 -> 6, 1 -> 2, 1 -> 3, 2 -> 7, 3 -> 9},DirectedEdges -> True]
Then ConnectedComponents works:
In[6]:= ConnectedComponents[g]
Out[6]= {{1}, {6}, {2}, {3}, {7}, {9}}
In[4]:= Head[g]
Out[4]= Graph