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2.3.11 Classes of studied networks Now, we detail classes of complex networks that have been observed in the real world. For more detail on these networks, we refer the reader to the survey by Newman [117]. Random networks have been heavily studied, starting with the seminal paper by Erd ̈os and R ́eyni [48]. These graphs are usually constructed by randomly adding links to a static set of nodes. Researchers have shown that random graphs tend to exhibit very short average path lengths between any two nodes [78]. More recent work on random graphs has provided mechanisms to construct graphs with specified degree distributions [108] and characterized the size of the large strongly connected component [109]. Power-law networks are networks where the probability that a node has degree k is proportional to k−α, for large k and α > 1. Thus, the degree distribution of a power-law network follows an exponential decay. The parameter α is called the power-law coefficient. Researchers have shown many real-world networks are power- law networks, including Internet topologies [51], the Web [15,83], social networks [4], neural networks [22], and power grids [128]. Scale-free networks are a class of power-law networks where the high-degree nodes tend to be connected to other high-degree nodes. Scale-free graphs are discussed in detail by Li et al. [91], and are defined as networks with a significant scale-free metric s(G). 30PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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