Systemic risk is a multifaceted concept that is of crucial importance for regulators. In order to ensure financial stability, they need to properly assess this risk, preventing financial shocks from affecting the real economy. In this study, we assess the consequences of the financialization of commodity markets by considering a system consisting of both commodity futures and financial markets in a sparse Vector AutoRegression (VAR) framework. It allows to distinguish two facets of systemic risk: the risk that all markets move at the same time (systematic risk, related to market integration) and the risk of propagation of shocks from one market to others. In addition, the combination of the sparsity of the model and of graph theory, we can build measures to assess the relative importance of both markets and their links. It is also possible to visualise the evolution of the markets over time, hence facilitating their monitoring. We first apply this methodology to our whole sample: 51 time series or returns, repres- enting 17 markets (3 maturities per asset) from 4 sectors (agriculture, energy, metals, finance) from 2000 to 2014. This static analysis on spot time series emphasises a sectorisation of those markets. Our results show the importance of the maturity dimensions when studying commodities, as they connect all the sectors and thus cause the integration of the whole system. In a dynamic analysis, we first give a broad overview of the evolution of the system in our sample and then focus notably on intriguing events in October 2008, shortly after the default of Lehman Brothers. The largest variations of the S&P500 index are followed, on the next day, by the largest price variations of some commodities. We find that the main component of systemic risk was integration, not propagation. This implies that, contrary to what we could think, financial shocks did not directly affect commodities.