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2.3 How do we analyze complex networks? We now discuss the various ways of analyzing and characterizing the shape of large networks, and conclude with a discussion of the various classes of graphs that have been observed in the real world. 2.3.1 Preliminaries We assume that we have a network which can be viewed as a graph G = (V, E). In the context of an online social network, for example, the vertices represent users and the edges represent relationships among users. The links in the graph can either be directed, meaning each link is sourced at one node and terminated at another node, or undirected, meaning each link is between two nodes without a source and destination. Consistent with previous work, we define a node i’s degree, denoted by di, to be the number of links the node has to other nodes. For directed networks, we distin- guish between indegree (the number of incoming links) and outdegree (the number of outgoing links). Also for directed networks, we consider the level of symmetry in the network to be the fraction of links that have a corresponding reverse link. 2.3.2 Radius and diameter We now discuss the radius and diameter of a graph, which represents how far away nodes are from each other in the network. First, the eccentricity of a node v is the maximal shortest path distance between v and any other node. The radius of a graph 23PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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