Starting from a relational database that gathers information on people mobility – such as origin/destination places, date and time, means of transport – as well as demographic data, we adopt a graph-based representation that results from the aggregation of individual travels. In such a graph, the vertices are places or points of interest (POI) and the edges stand for the trips. Travel information as well as user demographics are labels associated to the edges. We tackle the problem of discovering exceptional contextual subgraphs, i.e., subgraphs related to a context – a restriction on the attribute values – that are unexpected according to a model. Previous work considers a simple model based on the number of trips associated with an edge without taking into account its length or the surrounding demography. In this article, we consider richer models based on statistical physics and demonstrate their ability to capture complex phenomena which were previously ignored.