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Recommender systems are fundamental information filtering techniques to recommend content or items that meet users' personalities and potential needs. As a crucial solution to address the difficulty of user identification and unavailability of historical information, session-based recommender systems provide recommendation services that only rely on users' behaviors in the current session. However, most existing studies are not well-designed for modeling heterogeneous user behaviors and capturing the relationships between them in practical scenarios. To fill this gap, in this paper, we propose a novel graph-based method, namely Heterogeneous Information Crossing on Graphs (HICG). HICG utilizes multiple types of user behaviors in the sessions to construct heterogeneous graphs, and captures users' current interests with their long-term preferences by effectively crossing the heterogeneous information on the graphs. In addition, we also propose an enhanced version, named HICG-CL, which incorporates contrastive learning (CL) technique to enhance item representation ability. By utilizing the item co-occurrence relationships across different sessions, HICG-CL improves the recommendation performance of HICG. We conduct extensive experiments on three real-world recommendation datasets, and the results verify that (i) HICG achieves the state-of-the-art performance by utilizing multiple types of behaviors on the heterogeneous graph. (ii) HICG-CL further significantly improves the recommendation performance of HICG by the proposed contrastive learning module.