We propose a computationally efficient procedure for elevated mean detection on a connected subgraph of a network with node-related scalar observations. Our approach relies on two intuitions: first, a significant concentration of high observations in a connected subgraph implies that the subgraph induced by the nodes associated with the highest observations has a large connected component. Secondly, a greater detection power can be obtained in certain cases by denoising the observations using the network structure. Numerical experiments show that our procedure's detection performance and computational efficiency are both competitive.