Is there an efficient way to find the induced subgraph with the largest number of edges among all the induced subgraphs of the same size? For example, I have a 200-node graph H and I would like to find a 100-node induced subgraph that has the most edges.
2026-03-27 03:42:30.1774582950
Induced Subgraph with the Largest Number of Edges
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No (as long as $P \neq NP$). Suppose such an algorithm existed. Now, given a graph $G$ and an input $k$, we apply the putative procedure to find the densest $k$-vertex subgraph. This subgraph will be a $k$-clique if and only if $G$ contains a $k$-clique. Determining whether a graph has a $k$-clique is a standard NP-complete problem https://en.wikipedia.org/wiki/Clique_problem . Therefore your question is NP-hard.