Social messages classification is a research domain that has attracted the attention of many researchers in these last years. Indeed, the social message is different from ordinary text because it has some special characteristics like its shortness. Then the development of new approaches for the processing of the social message is now essential to make its classification more efficient. In this paper, we are mainly interested in the classification of social messages based on their spreading on online social networks (OSN). We proposed a new distance metric based on the Dynamic Time Warping distance and we use it with the probabilistic and the evidential k Nearest Neighbors (k-NN) classifiers to classify propagation networks (PrNets) of messages. The propagation network is a directed acyclic graph (DAG) that is used to record propagation traces of the message, the traversed links and their types. We tested the proposed metric with the chosen k-NN classifiers on real world propagation traces that were collected from Twitter social network and we got good classification accuracies.