This study approaches a robustification method for a multi-robot network connectivity. Instead of the vertex connectivity, which is commonly used as a robustness index, here we consider the size of the connected component remaining after one robot has been removed from the network, and we propose a distributed control law for improvement and preservation of the remaining connected component size. Some conditions of a modified graph Laplacian eigenvalue are analyzed for the improvement and the preservation, and then the control strategy is composed using the Laplacian eigenvalue as an indicator of the remaining connected component size. From simulations, we observed that a multi-robot system with our control method achieves a convincing state regarding the trade-off between a network robustness and a coverage task performance. Copyright (C) 2020 The Authors.