The aim of the article is to analyze graphs of weakly correlated stockreturns. The characteristics of these graphs such as number of edges, his-togram of vertices degrees, degrees distribution, hubs and independentsets are investigated. Pearson correlation and Kendall correlation areused to construct these graphs. Graph constructed by traditional proce-dure and graph constructed by Holm procedure are compared. Obtainedresults are exemplified on the data of France stock market. In particular itis shown that reliable maximum independent sets contain very few nodesdespite from the big size of set of weakly correlated pairs of stock returns.