On maximizing diffusion speed in social networks: impact of random seeding and clustering

A variety of models have been proposed and analyzed to understand how a new innovation (e.g., a technology, a product, or even a behavior) diffuses over a social network, broadly classified into either of epidemic-based or game-based ones. In this paper, we consider a game-based model, where each individual makes a selfish, rational choice in terms of its payoff in adopting the new innovation, but with some noise. We study how diffusion effect can be maximized by seeding a subset of individuals (within a given budget), i.e., convincing them to pre-adopt a new innovation. In particular, we aim at finding `good' seeds for minimizing the time to infect all others, i.e., diffusion speed maximization. To this end, we design polynomial-time approximation algorithms for three representative classes, Erdőos-Réenyi, planted partition and geometrically structured graph models, which correspond to globally well-connected, locally well-connected with large clusters and locally well-connected with small clusters, respectively, provide their performance guarantee in terms of approximation and complexity. First, for the dense Erdős-Rényi and planted partition graphs, we show that an arbitrary seeding and a simple seeding proportional to the size of clusters are almost optimal with high probability. Second, for geometrically structured sparse graphs, including planar and d-dimensional graphs, our algorithm that (a) constructs clusters, (b) seeds the border individuals among clusters, and (c) greedily seeds inside each cluster always outputs an almost optimal solution. We validate our theoretical findings with extensive simulations under a real social graph. We believe that our results provide new practical insights on how to seed over a social network depending on its connection structure, where individuals rationally adopt a new innovation. To our best knowledge, we are the first to study such diffusion speed maximization on the game-based diffusion, while the extensive research efforts have been made in epidemic-based models, often referred to as influence maximization.