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
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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. In networks, contagions such as information, purchasing behaviors, and diseases, spread and diffuse from node to node over the edges of the network. Moreover, in real-world scenarios multiple contagions spread through the network simultaneously. These contagions not only propagate at the same time but they also interact and compete with each other as they spread over the network. While traditional empirical studies and models of diffusion consider individual contagions as independent and thus spreading in isolation, we study how different contagions interact with each other as they spread through the network. We develop a statistical model that allows for competition as well as cooperation of different contagions in information diffusion. Competing contagions decrease each other's probability of spreading, while cooperating contagions help each other in being adopted throughout the network. We evaluate our model on 18,000 contagions simultaneously spreading through the Twitter network. Our model learns how different contagions interact with each other and then uses these interactions to more accurately predict the diffusion of a contagion through the network. Moreover, the model also provides a compelling hypothesis for the principles that govern content interaction in information diffusion. Most importantly, we find very strong effects of interactions between contagions. Interactions cause a relative change in the spreading probability of a contagion by em 71 on the average. Identifying the most influential individuals spreading ideas, information, or infectious diseases is a topic receiving significant attention from network researchers, since such identification can assist or hinder information dissemination, product exposure, and contagious disease detection. Hub nodes, high betweenness nodes, high closeness nodes, and high k-shell nodes have been identified as good initial spreaders. However, few efforts have been made to use node diversity within network structures to measure spreading ability. The two-step framework described in this paper uses a robust and reliable measure that combines global diversity and local features to identify the most influential network nodes. Results from a series of Susceptible–Infected–Recovered (SIR) epidemic simulations indicate that our proposed method performs well and stably in single initial spreader scenarios associated with various complex network datasets. Given a network of who-contacts-whom or who-links-to-whom, will a contagious virus product meme spread and ‘take over’ (cause an epidemic) or die out quickly? What will change if nodes have partial, temporary or permanent immunity? The epidemic threshold is the minimum level of virulence to prevent a viral contagion from dying out quickly and determining it is a fundamental question in epidemiology and related areas. Most earlier work focuses either on special types of graphs or on specific epidemiological cascade models. We are the first to show the G2-threshold (twice generalized) theorem, which nicely de-couples the effect of the topology and the virus model. Our result unifies and includes as special case older results and shows that the threshold depends on the first eigenvalue of the connectivity matrix, (a) for any graph and (b) for all propagation models in standard literature (more than 25, including H.I.V.). Our discovery has broad implications for the vulnerability of real, complex networks and numerous applications, including viral marketing, blog dynamics, influence propagation, easy answers to ‘what-if’ questions, and simplified design and evaluation of immunization policies. We also demonstrate our result using extensive simulations on real networks, including on one of the biggest available social-contact graphs containing more than 31 million interactions among more than 1 million people representing the city of Portland, Oregon, USA.