We consider the following general family of algorithmic problems that arises in transcriptomics, metabolomics and other fields: given a weighted graph G and a subset of its nodes S, find subsets of S that show significant connectedness within G. A specific solution to this problem may be defined by devising a scoring function, the Maximum Clique problem being a classic example, where S includes all nodes in G and where the score is defined by the size of the largest subset of S fully connected within G. Major practical obstacles for the plethora of algorithms addressing this type of problem include computational efficiency and, particularly for more complex scores which take edge weights into account, the computational cost of permutation testing, a statistical procedure required to obtain a bound on the p-value for a connectedness score. To address these problems, we developed CTD, "Connect the Dots", a fast algorithm based on data compression that detects highly connected subsets within S. CTD provides information-theoretic upper bounds on p-values when S contains a small fraction of nodes in G without requiring computationally costly permutation testing. We apply the CTD algorithm to interpret multi-metabolite perturbations due to inborn errors of metabolism and multi-transcript perturbations associated with breast cancer in the context of disease-specific Gaussian Markov Random Field networks learned directly from respective molecular profiling data.