On maximizing diffusion speed in social networks

Abstract

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, Erdős-Rényi, 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 epidemicbased models, often referred to as influence maximization.

Tree Sampling for Detection of Information Source in Densely Connected Networks

“…The dynamics of the spreading process have been studied in [6][7][8][9]. In [6], the information source detection under the Susceptible-Infected-Recovered (SIR) epidemic model has been considered.…”

“…The authors have shown that the half-life time of virus over two simple networks of clique networks and star networks is O( log n n ) and O(log n), respectively, where n is the number of infected nodes. Besides epidemic models, a game-based model has been studied in [9], where each node can adopt the information to maximize its payoff. The work aims to find good seeds (i.e., information sources) that can maximize the diffusion speed and developed interesting seeding schemes for different network structures.…”

“…Although there have been several studies on the information source detection in the literature [1][2][3][4][5][6][7][8][9], most of them have assumed a specific type of network topology, i.e., trees, and cannot be directly applied to a more general network topology that most social networking services have. Their extension to general networks is not straightforward and often suffers from high computational complexity.…”

Probabilistic Diffusion in Random Network Graphs

“…In [6], the authors propose a probabilistic approach of social influence diffusion model with incentives (as uniform diffusion has been observed to be no longer valid in social networks and high degree nodes need not be the most influential in all contexts [12]); the authors propose an influence diffusion probability for each node, instead of uniform probability, and categorize nodes into two classes: active and inactive; the active nodes have chances of influencing the inactive nodes, but not vice-versa; diffusion still happens based on a system-wide threshold. Our probabilistic diffusion model is link-based (could be even run with different diffusion probability for each link) and does not use any node-based system-wide threshold to regulate the diffusion.…”

Rapid Mixing Swendsen-Wang Sampler for Stochastic Partitioned Attractive Models

“…Moreover, the non-negative restricted Boltzmann machine (RBM), which is equivalent to FIM on complete bipartite graphs, has been studied in the context of unsupervised deep learning models [33], where non-negativity (i.e., ferromagneticity) provides non-negative matrix factorization [23] like interpretable features, which is especially useful for analyzing medical data [41,26] and document data [33]. FIM is also a popular model for studying strategic diffusion in social networks [35,29], where in this case β uv represents a friendship or other positive relationships between two individuals u, v.…”