Cascades and Myopic Routing in Nonhomogeneous Kleinberg's Small World Model

Kleinberg’s small world model [20] simulates social networks with both strong and weak ties. In his original paper, Kleinberg showed how the distribution of weak-ties, parameterized by \(\gamma \), influences the efficacy of myopic routing on the network. Recent work on social influence by k-complex contagion models discovered that the distribution of weak-ties also impacts the spreading rate in a crucial manner on Kleinberg’s small world model [15]. In both cases the parameter of \(\gamma = 2\) proves special: when \(\gamma \) is anything but 2 the properties no longer hold.

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