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In the context of online social networks, the linkage graph-- a graph composed of social links--has been studied for several years, while researchers have recently suggested studying the activity graph of real user interactions. Understanding these two types of graphs is important since different online applications might rely on different underlying structures. In this paper, we first analyze two specific online social networks, one of which stands for a linkage graph and the other for an activity graph. Based on our analysis, we find that the two networks exhibit several static and dynamic properties in common, but show significant difference in degree correlation. This property of degree correlation is further confirmed as a key distinction between these two types of graphs. To further understand this difference, we propose a network generator which could as well capture the other examined properties. Finally, we provide some potential implications of our findings and generator.