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In the densest subgraph problem, given a weighted undirected graph G(V,E,w), with non-negative edge weights, we are asked to find a subset of nodes S⊆ V that maximizes the degree density w(S)/|S|, where w(S) is the sum of the edge weights induced by S. This problem is a well studied problem, known as the densest subgraph problem, and is solvable in polynomial time. But what happens when the edge weights are negative? Is the problem still solvable in polynomial time? Also, why should we carearXiv:1904.08178v1 fatcat:5q3kcvzzcvfpzg6tu5kg6h7a4e