# R p o t e n t i a l c l i q u e p candidates f o r i

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R \\ p o t e n t i a l c l i q u e P \\ candidates f o r i n c l u s i o n X \\ previously found v e r t i c e s ( excluded ) BronKerbosch (R,P,X) : i f P and X are both empty : report R as a maximal c l i q u e f o r each vertex v in P: BronKerbosch1 ( R ∪ { v } , P N ( v ) , X N ( v )) P := P \ { v } X := X ∪ { v } This algorithm is slow, so you will not be able to run it on the entire friend graph. Instead, use 50.json See h ttp://en.wikipedia.org/wiki/Bron-Kerbosch algorithm for more information. 8

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5 Phase 4: Summary 5.1 Questions.txt 35pts Take another breather; it’s time to reflect on what you’ve learned. Please submit a Questions.txt file with the answers, in order, to the following problems. 1. You computed the set of connected components for both the original graph, as well as the graph with the root removed. How did these sets differ? 2. What type of graph representation was contained in the JSON files? 3. Name three differences between the graph centrality measures, making reference to each one. 4. What is a clique? 5. How does the method in which we are generating edge weights impact/influence Dijkstra’s shortest path algorithm? 6. For the following algorithms, describe your code’s big-Oh runtime and explain if they’re running optimally: DFS BFS FakebookReader (graph creation) MST FakebookReader.getConnectedComponentsWithoutRoot() 7. Finally, write two pararaphs on design choices you made, justifying them in terms of runtime and space efficiency. 9
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