Maximum (edge)weight connected subgraph of an undirected graph. Let G be a undirected graph with weighted edges. I want to find a connected subgraph which has at most L nodes(vertices) whose sum of edges is maximum. It sounds similar to MWCS or PCST but here only the edges are weighted and there is a limit on no of nodes in the subgraph. These are related papers I found for solving MWCS or PCST:
http://dimacs11.cs.princeton.edu/workshop/ElKebirKlau.pdf
http://dimacs11.cs.princeton.edu/workshop/AlthausBlumenstock.pdf
PS: All weights are positive unlike in MWCS.

You might want take a look at our paper that considers what we call a generalized MWCS problem (https://arxiv.org/abs/1605.02168) and corresponding solver (https://github.com/ctlab/gmwcs-solver/). There, unlike in classical MWCS, edge weights (both postitve and negative) are allowed. It works pretty well for the practical instances that we have.
