Modern popular TV series often develop complex storylines spanning several seasons, but are usually watched in quite a discontinuous way. As a result, the viewer generally needs a comprehensive summary of the previous season plot before the new one starts. The generation of such summaries requires first to identify and characterize the dynamics of the series subplots. One way of doing so is to study the underlying social network of interactions between the characters involved in the narrative. The standard tools used in the Social Networks Analysis field to extract such a network rely on an integration of time, either over the whole considered period, or as a sequence of several time-slices. However, they turn out to be inappropriate in the case of TV series, due to the fact the scenes showed onscreen alternatively focus on parallel storylines, and do not necessarily respect a traditional chronology. This makes existing extraction methods inefficient to describe the dynamics of relationships between characters, or to get a relevant instantaneous view of the current social state in the plot. This is especially true for characters shown as interacting with each other at some previous point in the plot but temporarily neglected by the narrative. In this article, we introduce narrative smoothing, a novel, still exploratory, network extraction method. It smooths the relationship dynamics based on the plot properties, aiming at solving some of the limitations present in the standard approaches. In order to assess our method, we apply it to a new corpus of 3 popular TV series, and compare it to both standard approaches. Our results are promising, showing narrative smoothing leads to more relevant observations when it comes to the characterization of the protagonists and their relationships. It could be used as a basis for further modeling the intertwined storylines constituting TV series plots.