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91 -0.189, respectively [116]. On the other hand, many scientific coauthorship networks, a different type of social network, have been shown to have positive r [116]. Taken together, the significant scale-free metric and the positive assortativity coefficient suggests that there exists a tightly-connected “core” of the high-degree nodes which connect to each other, with the lower-degree nodes on the fringes of the network. In the next few sections, we explore the properties of these two components of the graph in detail. 5.7 Densely connected core We loosely define a core of a network as any (minimal) set of nodes that satisfies two properties. First, the core must be necessary for the connectivity of the network (i.e., removing the core breaks the remainder of the nodes into many small, discon- nected clusters). Second, the core must be strongly connected with a relatively small diameter. Thus, a “core” is a small group of well-connected group of nodes that is necessary to keep the remainder of the network connected. To more closely explore the core of the network, we use an approximation previ- ously used in Web graph analysis [23]. Specifically, we remove increasing numbers of the highest degree nodes and analyze the connectivity of the remaining graph.4 We calculate the size of the largest remaining SCC, which is the largest set of users who can mutually reach each other. 4The large size of the graphs we study makes a cut set analysis computationally infeasible.PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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