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From the proof of Theorem 34.12, we know that the vertex-cover problem and the NP-complete clique problem are complementary in the sense that an optimal vertex cover is the complement of a maximum-size clique in the complement graph. Does this relationship imply that there is a polynomial-time approximation algorithm with a constant approximation ratio for the clique problem? Justify your answer. | Numerade
From the proof of Theorem 34.12, we know that the vertex-cover pro…
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9.3. Modularity Resolution LimitConsider a network consisting of a ring of nc cliques, each clique havingNc nodes and m(m-1)/2 links. The neighboring cliques are connected by asingle link (Figure 9.34). The network has an obvious community structure,each community corresponding to a clique.(a) Determine the modularity Msingle of this natural partition, and themodularity Mpairs of the partition in which pairs of neighboringcliques are merged into a single community, as indicated by thedotted line
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