Complex networks can often be divided in dense sub-networks called communities. Using a partition edit distance, we study how three community detection algorithms transform their outputs if the input network is slightly modified. The instabilities appear to be important and we propose a modification of one algorithm to stabilize it and to allow the tracking of the communities in an evolving network. This modification has one parameter which is a tradeoff between stability and quality. The resulting algorithm appears to be very effective. We finally use it on an evolving network of blogs.