Minimal Power Graphs
In general, there is no unique minimal power graph for a given graph. In this example (right) a graph of four nodes and five edges admits two minimal power graphs of two power edges each. The main difference between these two minimal power graphs is the higher nesting level of the second power graph as well as a loss of symmetry with respect to the underlying graph. Loss of symmetry is only a problem in small toy examples since complex networks rarely exhibit such symmetries in the first place. Additionally, one can minimize the nesting level but even then, there is in general not a unique minimal power graph of minimal nesting level.
Read more about this topic: Power Graph Analysis
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