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In recent years, with the number of users of Internet increasing, user behavior on Internet becomes more and more complicated. Studies on Internet traffic are helpful for both analyzing user behavior and managing the Internet. In our paper, based on practical traffic data, we construct Internet flow graphs. Since high-degree nodes play a dominant role in the evolution of graphs, we concentrate on degree-related characteristics of the graph with high-degree nodes from the perspective of complex network. We mainly focus on five applications, i.e. P2P Download, P2P Stream, HTTP, Video Stream and Instant Messaging, and find that the high-degree nodes of P2P Download and P2P Stream prefer connecting either high-degree nodes or low-degree nodes, but few of them connect both high-degree nodes and low-degree nodes averagely.