We assess volatility spillovers and directional connectedness among stock returns of the biggest 20 oil companies listed in the New York Stock Exchange (NYSE) between January 2002 and November 2016. The methodological approach we employed allows the study of the total average connectedness, statically and dynamically, as well as pairwise spillovers within oil firms during the sampled period. For instance, estimation results on full sample connectedness measures show that the system average connectedness is 84.7%. Based on the net pairwise spillovers estimates, we construct risk network representations for days of abnormal behavior in oil prices. This allows the identification of potential shock transmitters and receivers within the sample. The estimates provided can be used for portfolio decision purposes and for designing regulatory policies.