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I have the following MRF graph and I need to find out about the clique factorization of the graph. I understand what it means for a graph to have a clique factorization. However it seems to be that it will not be unique. Is it true that that is the case? If not can I know how to get the clique factorization of the graph? Or is it not possible to know the clique factorization just from the graph itself?

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Your intuition is correct: one cannot read the factorization from the graph. In general, many different clique factorizations will induce the exact same graph.

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  • $\begingroup$ Could you give an explanation of why, or an example, or at least a reference? $\endgroup$ – kjetil b halvorsen Mar 22 '19 at 13:00

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