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 timeresolved 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

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The flow of information or influence through a large social network can be thought of as unfolding with the dynamics of an epidemic: as individuals become aware of new ideas, tech-nologies, fads, rumors, or gossip, they have the potential to pass them on to their friends and colleagues, causing the resulting behavior to cascade through the network. We consider a collection of probabilistic and game-theoretic models for such phenomena proposed in the mathematical social sciences, as well as recent algorithmic work on the problem by computer scientists. Building on this, we discuss the implications of cascading behavior in a number of on-line settings, including word-of-mouth effects (also known as “viral marketing”) in the success of new products, and the influence of social networks in the growth of on-line communities. 1

A central idea in marketing and diffusion research is that influentials—a minority of individuals who influence an exceptional number of their peers—are important to the formation of public opinion. Here we examine this idea, which we call the “influentials hypothesis,” using a series of computer simulations of interpersonal influence processes. Under most conditions that we consider, we find that large cascades of influence are driven not by influentials, but by a critical mass of easily influenced individuals. Although our results do not exclude the possibility that influentials can be important, they suggest that the influentials hypothesis requires more careful specification and testing than it has received.

We present a model of contagion that unifies and generalizes existing models of the spread of social influences and microorganismal infections. Our model incorporates individual memory of exposure to a contagious entity (e.g. a rumor or disease), variable magnitudes of exposure (dose sizes), and heterogeneity in the susceptibility of individuals. Through analysis and simulation, we examine in detail the case where individuals may recover from an infection and then immediately become susceptible again (analogous to the so-called SIS model). We identify three basic classes of contagion models which we call epidemic threshold, vanishing critical mass, and critical mass classes, where each class of models corresponds to different strategies for prevention or facilitation. We find that the conditions for a particular contagion model to belong to one of the these three classes depend only on memory length and the probabilities of being infected by one and two exposures, respectively. These parameters are in principle measurable for real contagious influences or entities, thus yielding empirical implications for our model. We also study the case where individuals attain permanent immunity once recovered, finding that epidemics inevitably die out but may be surprisingly persistent when individuals possess memory.

New ideas, products, and practices take time to diffuse, a fact that is often attributed to some form of heterogeneity among potential adopters. This paper examines three broad classes of diffusion models-- contagion, social influence, and social learning – and shows how to incorporate heterogeneity into each at a high level of generality without losing analytical tractability. Each type of model leaves a characteristic ‘footprint ’ on the shape of the adoption curve that provides a basis for discriminating empirically between them. The approach is illustrated using the classic study of Ryan and Gross on the diffusion of hybrid corn (JEL O33, D8, M3).

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. 1

One method of viral marketing involves seeding certain consumers within a population to encourage faster adoption of the product throughout the entire population. However, determining how many and which consumers within a particular social network should be seeded to maximize adoption is challenging. We define a strategy space for consumer seeding by weighting a combination of network characteristics such as average path length, clustering coefficient, and degree. We measure strategy effectiveness by simulating adoption on a Bass-like agent-based model, with five different social network structures: four classic theoretical models (random, lattice, small-world, and preferential attachment) and one empirical (extracted from Twitter friendship data). To discover good seeding strategies, we have developed a new tool, called BehaviorSearch, which uses genetic algorithms to search through the parameter-space of agent-based models. This evolutionary search also provides insight into the interaction between strategies and network structure. Our results show that one simple strategy (ranking by node degree) is near-optimal for the four theoretical networks, but that a more nuanced strategy performs significantly better on the empirical Twitter-based network. We also find a correlation between the optimal seeding budget for a network, and the inequality of the degree distribution.

Are large biological extinctions such as the Cretaceous/Tertiary KT boundary due to a meteorite, extreme volcanic activity or self-organized critical extinction cascades? Are commercial successes due to a progressive reputation cascade or the result of a well orchestrated advertisement? Determining the chain of causality for extreme events in complex systems requires disentangling interwoven exogenous and endogenous contributions with either no clear or too many signatures. Here, I review several efforts carried out with collaborators, which suggest a general strategy for understanding the organization of several complex systems under the dual effect of endogenous and exogenous fluctuations. The studied examples are: Internet download shocks, book sale shocks, social shocks, financial volatility shocks, and financial crashes. Simple models are offered to quantitatively relate the endogenous organization to the exogenous response of the system. Suggestions for applications of these ideas to many other systems are offered. 1

Abstract. Ad hoc networks can be formed from arbitrary collections of individual people (forming online computer-mediated communities), mobile routers (forming data communication networks) or electronic business processes (forming virtual enterprises). One way to deal with common features of dynamism in the network topology and membership, conflicts, sub-ideal operation, security, and the general need for continuous operation in the absence of a centralised facility, is to treat the ad hoc network as a normgoverned multi-agent system and use participatory adaptation as the mechanism for achieving autonomic capability (i.e. a global system response derived from the collective local behaviours and interactions of the individuals comprising the system). Therefore, complementing the formal representation of organisational behaviour defined in terms of roles, rules, norms, etc., this autonomic capability is at least partially derived from an underlying social network which plays a significant role in determining how, for example, conflicts are resolved and how the organisation itself is run. This position statement presents initial developments in what we call micro-social systems, which arise from interleaving a logical model of norm-governed systems with a mathematical model of social networks, and its application to issues of resource allocation, security, conflict resolution and self-adaptation in ad hoc networks. 1