Reflect/invert unidirect graph edges

Given is a graph with data in mathematica-11. The graph includes undirected edges between nodes and standalone nodes (not connected).

Graph[{1 <-> 2, 2<-> 3, 3<-> 1, 4<-> 5, 5<-> 6, 6<-> 2, 2<-> 4}, VertexLabels -> "Name", VertexShapeFunction -> "Diamond", VertexSize -> Small]

Question:

How do I reflect (invert) the edges between the nodes?

Since they are unidirected, by reflecting/inverting I mean that those nodes are supposed to be linked where no edge was before (and the former edges are gone).

Mathematica-11 provides the ReverseGraph function, however this one does only reflect directed edges by their direction. Any ideas?

Idea:

Convert the graph into a AdjacencyMatrix and inverse it. Then, the inversed matrix could be used to create the reflected/inverted graph. However, I am stuck with inverting the AdjacencyMatrix since the result will behavior strange:

So simple the true values are replaced with the term inverse when using Inverse (AdjacencyMatrix[data]) // MatrixForm

Related:

This article covers how to reflect edge weights, but not the edges itself.

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I'm not sure I completely understand your question so if this isn't the answer tell us why not:

opts = {VertexLabels -> "Name", VertexShapeFunction -> "Diamond", VertexSize -> Small}

g1 = Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1, 4 <-> 5, 5 <-> 6, 6 <-> 2, 2 <-> 4}];

Then you might like

GraphComplement[g1, opts]

or, if you want edges from each node to itself

AdjacencyGraph[Table[1, {VertexCount[g1]}, {VertexCount[g1]}] - AdjacencyMatrix[g1], opts]

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