Theoretical progress in understanding the dynamics of spreading processes on graphs suggests the existence of an epidemic threshold below which no epidemics form and above which epidemics spread to a significant fraction of the graph. We have observed information cascades on the social media site Digg that spread fast enough for one initial spreader to infect hundreds of people, yet end up affecting only 0.1 of the entire network. We find that two effects, previously studied in isolation, combine cooperatively to drastically limit the final size of cascades on Digg. First, because of the highly clustered structure of the Digg network, most people who are aware of a story have been exposed to it via multiple friends. This structure lowers the epidemic threshold while moderately slowing the overall growth of cascades. In addition, we find that the mechanism for social contagion on Digg points to a fundamental difference between information spread and other contagion processes: despite multiple opportunities for infection within a social group, people are less likely to become spreaders of information with repeated exposure. The consequences of this mechanism become more pronounced for more clustered graphs. Ultimately, this effect severely curtails the size of social epidemics on Digg.
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. Social networks evolve over time, driven by the shared activities and affiliations of their members, by similarity of individuals' attributes, and by the closure of short network cycles. We analyzed a dynamic social network comprising 43,553 students, faculty, and staff at a large university, in which interactions between individuals are inferred from time-stamped e-mail headers recorded over one academic year and are matched with affiliations and attributes. We found that network evolution is dominated by a combination of effects arising from network topology itself and the organizational structure in which the network is embedded. In the absence of global perturbations, average network properties appear to approach an equilibrium state, whereas individual properties are unstable.  The processes by which communities come together, attract new members, and develop over time is a central research issue in the social sciences - political movements, professional organizations, and religious denominations all provide fundamental examples of such communities. In the digital domain, on-line groups are becoming increasingly prominent due to the growth of community and social networking sites such as MySpace and LiveJournal. However, the challenge of collecting and analyzing large-scale time-resolved data on social groups and communities has left most basic questions about the evolution of such groups largely unresolved: what are the structural features that influence whether individuals will join communities, which communities will grow rapidly, and how do the overlaps among pairs of communities change over time.Here we address these questions using two large sources of data: friendship links and community membership on LiveJournal, and co-authorship and conference publications in DBLP. Both of these datasets provide explicit user-defined communities, where conferences serve as proxies for communities in DBLP. We study how the evolution of these communities relates to properties such as the structure of the underlying social networks. We find that the propensity of individuals to join communities, and of communities to grow rapidly, depends in subtle ways on the underlying network structure. For example, the tendency of an individual to join a community is influenced not just by the number of friends he or she has within the community, but also crucially by how those friends are connected to one another. We use decision-tree techniques to identify the most significant structural determinants of these properties. We also develop a novel methodology for measuring movement of individuals between communities, and show how such movements are closely aligned with changes in the topics of interest within the communities.