## A Simple Model of Cascades in Networks

Date: 07 November 2016

We consider a linear threshold model of cascades in networks. An agent switches (e.g. adopts an innovation) if the proportion of his neighbors who have already switched exceeds his threshold. Agents’ thresholds are drawn randomly at the start of the cascade process. We present a result for the expected number of switches in arbitrary finite networks with any initial seeds. We define a new measure of an agent’s ability to influence a cascade in a given network, called cascade centrality, which is the expected size of the cascade when the agent is the only seed in the network. We then define contagion centrality, which is the probability that all agents switch when the node is a seed. For certain network topologies, we find ...#### A Simple Model of Cascades in Networks

Type: paper

Lim, Y., Ozdaglar, A. & Teytelboym, A. (2016). ‘A Simple Model of Cascades in Networks’. Submitted. Available at http://t8el.com/wp-content/uploads/2015/08/SimpleCascades.pdf

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