You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We present an analysis of a person-to-person recommendation network, consisting of 4 million people who made 16 million recommendations on half a million products. We observe the propagation of recommendations and the cascade sizes, which we explain by a simple stochastic model. We analyze how user behavior varies within user communities defined by a recommendation network. Product purchases follow a ‘long tail’ where a significant share of purchases belongs to rarely sold items. We establish how the recommendation network grows over time and how effective it is from the viewpoint of the sender and receiver of the recommendations. While on average recommendations are not very effective at inducing purchases and do not spread very far, we present a model that successfully identifies communities, product, and pricing categories for which viral marketing seems to be very effective.

Cited Abstract(s):
[1]: 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).

[2]: We present a dynamical theory of opinion formation that takes explicitly into account the structure of the social network in which individuals are embedded. The theory predicts the evolution of a set of opinions through the social network and establishes the existence of a martingale property, i.e. the expected weighted fraction of the population that holds a given opinion is constant in time. Most importantly, this weighted fraction is not either zero or one, but corresponds to a non- trivial distribution of opinions in the long time limit. This coexistence of opinions within a social network is in agreement with the often observed locality effect, in which an opinion or a fad is localized to given groups without infecting the whole society. We verified these predictions as well as others concerning the fragility of opinions and the importance of highly connected individuals by computer experiments on scale-free networks.

[3]: The strength of weak ties is that they tend to be long—they connect socially distant locations, allowing information to diffuse rapidly. The authors test whether this “strength of weak ties” generalizes from simple to complex contagions. Complex contagions require social affirmation from multiple sources. Examples include the spread of high‐risk social movements, avant garde fashions, and unproven technologies. Results show that as adoption thresholds increase, long ties can impede diffusion. Complex contagions depend primarily on the width of the bridges across a network, not just their length. Wide bridges are a characteristic feature of many spatial networks, which may account in part for the widely observed tendency for social movements to diffuse spatially.

[4]: Models of the convergence of opinion in social systems have been the subject of considerable recent attention in the physics literature. These models divide into two classes, those in which individuals form their beliefs based on the opinions of their neighbors in a social network of personal acquaintances, and those in which, conversely, network connections form between individuals of similar beliefs. While both of these processes can give rise to realistic levels of agreement between acquaintances, practical experience suggests that opinion formation in the real world is not a result of one process or the other, but a combination of the two. Here we present a simple model of this combination, with a single parameter controlling the balance of the two processes. We find that the model undergoes a continuous phase transition as this parameter is varied, from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion.
In the independent cascade model, [1] simulated the spread of information on an artificially generated network topology that consisted both of strong ties within groups of spatially proximate nodes and weak ties between the groups. They found that weak ties were important to the rate of information diffusion. Centola and Macy [3] modeled product adoption on small world topologies when a person's chance of adoption is dependent on having more than one contact who had previously adopted. Wu and Huberman [2] modeled opinion formation on different network topologies, and found that if highly connected nodes were seeded with a particular opinion, this would proportionally effect the long term distribution of opinions in the network. Holme and Newman [4] introduced a model where individuals' preferences are shaped by their social networks, but their choices of whom to include in their social network are also influenced by their preferences.