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Original Graph, G

5. 6. 7. S T O P. 1. 8. 3. 2. 9. 4. 5. Protein. Maximal clique. 2. Fill-in edge. Original Graph, G. Graph modification. Modified Graph, G*. Is the modified graph chordal?. 1. Add edges between nodes with identical set of neighbors 2. Eliminate squares (4-cycles)

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Original Graph, G

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  1. 5 6 7 S T O P 1 8 3 2 9 4 5 Protein Maximal clique 2 Fill-in edge Original Graph, G Graph modification Modified Graph, G* Is the modified graph chordal? 1. Add edges between nodes with identical set of neighbors 2. Eliminate squares (4-cycles) (if any) by adding a (restricted) set of “fill in” edges connecting nodes with similar set of neighbors 5 6 7 No 1 10 8 10 3 2 9 4 Yes Compute all clique tree representations of the modified graph. Tree of Complexes Clique Tree of G* 5, 6, 8 1, 2, 8, 9 6, 10 1, 2, 5, 8 1,2,3,4 5, 7, 8 1 8

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