I have a graph related problem. Let $G$ be an undirected weighted graph of $N$ nodes. I want to find $p$ independent (they have no edge linking them) sub-graphs of $m$ nodes in a way that the total weight is maximized.
For example, let $G$ be a graph of $16$ nodes, I want to find $4$ sub-graphs of $4$ nodes with $w_1, w_2, w_3, w_4$ as their weights (sum of the weights on the subgraph's edges) I want to determine the $4$ subgraphs that will maximize $w_1+w_2+w_3+w_4$.
Is this a classic graph problem? Is there already an algorithm for this? I am not very experienced with graphs and my research on the net was only confusing. Any ideas on how to approach this?
Thank you for your help