We propose a stochastic model for the diffusion of topics entering a social network modeled by a Watts-Strogatz graph. Our model sets into play an implicit competition between these topics as they vie for the attention of users in the network. The dynamics of our model are based on notions taken from real-world OSNs like Twitter where users either adopt an exogenous topic or copy topics from their neighbors leading to endogenous propagation. When instantiated correctly, the model achieves a viral regime where a few topics garner unusually good response from the network, closely mimicking the behavior of real-world OSNs. Our main contribution is our description of how clusters of proximate users that have spoken on the topic merge to form a large giant component making a topic go viral. This demonstrates that it is not weak ties but actually strong ties that play a major part in virality. We further validate our model and our hypotheses about its behavior by comparing our simulation results with the results of a measurement study conducted on real data taken from Twitter.
The relevance of a local density of links in spreading a contagion has been studied in the past under the header of complex propagation @cite_13 @cite_5 . These models show that when simultaneous existence of multiple activators is required for a node to get infected, long range links and randomness can slow down the propagation. The relevance of a clustered local community for sustenance has also been propounded by Young @cite_21 in the context of the spread of innovation. Goldenberg et. al. @cite_20 come to a somewhat contradictory conclusion, claiming that strong and weak ties are equally important in product adoption through word-of-mouth.
@cite_5 @cite_21 @cite_13 @cite_20
2155796078 2016468753 1495750374
Social norms and institutions are mechanisms that facilitate coordination between individuals. A social innovation is a novel mechanism that increases the welfare of the individuals who adopt it compared with the status quo. We model the dynamics of social innovation as a coordination game played on a network. Individuals experiment with a novel strategy that would increase their payoffs provided that it is also adopted by their neighbors. The rate at which a social innovation spreads depends on three factors: the topology of the network and in particular the extent to which agents interact in small local clusters, the payoff gain of the innovation relative to the status quo, and the amount of noise in the best response process. The analysis shows that local clustering greatly enhances the speed with which social innovations spread. It also suggests that the welfare gains from innovation are more likely to occur in large jumps than in a series of small incremental improvements. Random links between otherwise distant nodes can greatly facilitate the propagation of disease or information, provided contagion can be transmitted by a single active node. However, we show that when the propagation requires simultaneous exposure to multiple sources of activation, called complex propagation, the effect of random links can be just the opposite; it can make the propagation more difficult to achieve. We numerically calculate critical points for a threshold model using several classes of complex networks, including an empirical social network. We also provide an estimation of the critical values in terms of vulnerable nodes. Though word-of-mouth (w-o-m) communications is a pervasive and intriguing phenomenon, little is known on its underlying process of personal communications. Moreover as marketers are getting more interested in harnessing the power of w-o-m, for e-business and other net related activities, the effects of the different communications types on macro level marketing is becoming critical. In particular we are interested in the breakdown of the personal communication between closer and stronger communications that are within an individual's own personal group (strong ties) and weaker and less personal communications that an individual makes with a wide set of other acquaintances and colleagues (weak ties).