Complex Contagion refers to the phenomenon in social network

Social network

A social network is a social structure made up of individuals called "nodes", which are tied by one or more specific types of interdependency, such as friendship, kinship, common interest, financial exchange, dislike, sexual relationships, or relationships of beliefs, knowledge or prestige.Social...

s in which multiple sources of exposure to an innovation are required before an individual adopts the change of behavior. This differs from simple contagion in that, unlike a disease, it may not be possible for the innovation to spread after only one incident of contact with an infected neighbor. The spread of complex contagion across a network of people may depend on many social and economic factors; for instance, how many of one's friends adopt the new idea as well as how many of them don't can influence the individual, as well as their own disposition in embracing change.

Mechanisms of Complex Contagion

Complex Contagion and the Weakness of Long Ties by Damon Centola of Harvard University

Harvard University

Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...

 and Michael Macy of Cornell University

Cornell University

Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...

 suggests four mechanisms of complex contagion. These properties explain the need for multiple exposures in the spread of contagion.

1. Strategic complementarity. Many innovations are costly, especially for early adopters but less so for those who wait. The same holds for participation in collective action
   Collective action
   Collective action is the pursuit of a goal or set of goals by more than one person. It is a term which has formulations and theories in many areas of the social sciences.-In sociology:...
   
   .
2. Credibility. Innovations often lack credibility until adopted by neighbors. Hearing the same story from different people makes it seem less likely that surprising information is nothing more than the fanciful invention of the informant.
3. Legitimacy. Knowing that a movement exists or that a collective action will taken place is rarely sufficient to induce bystanders to join in. Having several close friends participate in an event often greatly increases an individual’s likelihood of also joining, especially for high-risk social movement
   Social movement
   Social movements are a type of group action. They are large informal groupings of individuals or organizations focused on specific political or social issues, in other words, on carrying out, resisting or undoing a social change....
   
   s. Innovators risk being shunned as deviants until there is a critical mass of early adopters, and non-adopters are likely to challenge the legitimacy of the innovation.
4. Emotional contagion
   Emotional contagion
   Emotional contagion is the tendency to catch and feel emotions that are similar to and influenced by those of others. One view developed by John Cacioppo of the underlying mechanism is that it represents a tendency to automatically mimic and synchronize facial expressions, vocalizations, postures,...
   
   . Most theoretical models of collective behavior
   Collective behavior
   The expression collective behaviour was first used by Robert E. Park, and employed definitively by Herbert Blumer, to refer to social processes and events which do not reflect existing social structure , but which emerge in a "spontaneous" way.Collective behavior might also be defined as action...
   
    – from action theory
   Action theory (sociology)
   In sociology, action theory refers to the theory of social action presented by the American theorist Talcott Parsons.Parsons established action theory in order to integrate the study of social order with the structural and voluntaristic aspects of macro and micro factors...
   
    to threshold model
   Threshold model
   In mathematical or statistical modelling a threshold model is any model where a threshold value, or set of threshold values, is used to distinguish ranges of values where the behaviour predicted by the model differs in some important way...
   
   s to cybernetics
   Cybernetics
   Cybernetics is the interdisciplinary study of the structure of regulatory systems. Cybernetics is closely related to information theory, control theory and systems theory, at least in its first-order form...
   
    share the basic assumption that there are expressive and symbolic impulses in human behavior
   Human behavior
   Human behavior refers to the range of behaviors exhibited by humans and which are influenced by culture, attitudes, emotions, values, ethics, authority, rapport, hypnosis, persuasion, coercion and/or genetics....
   
    that can be communicated and amplified in spatially and socially concentrated gatherings.

Contested vs. Uncontested

Uncontested

The spread of the contagion is dependent solely on the number of people you are connected to who are different from your own state. You are not hindered whatsoever by the number of people in the same state as you. Generally, the more neighbors an individual has, the greater the chance of the individual adopting the innovation if the spread is uncontested.

Contested

The spread of the contagion is dependent on both the adamancy of those who are in a different state from your own as well as the countervailing influence of those who share your current state. In this case, the more neighbors an individual has, the smaller the chance of the individual adopting the innovation.

Diffusion and Cascading Behaviors in Networks

Consider a graph

Graph (mathematics)

In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges...

 of any reasonable size. Node v’s neighbors can be split into 2 sets: Set A contains v's neighbors who have adopted a new behavior and B is the set of those behaving conservatively. Node v will only adopt the behavior of those in A if at least a q fraction of neighbors follow behavior A.

• if q is small, the behavior is easily adopted and easily spread
• if q is large, B is an attractive behavior and it takes more friends to engage in A before v will switch.

Cascading - diffusion over the entire network : Consider a set of initial adopters who start with a new behavior A, while every other node starts with behavior B. Nodes then repeatedly evaluate the decision to switch from B to A using a threshold of q. If the resulting cascade of adoptions of A eventually causes every node to switch from B to A, then we say that the set of initial adopters causes a complete cascade at threshold q. Clusters of density d > 1-q are obstacles to cascades across the entire network.

Application and Examples

Many of our interactions with the rest of the world happen at a local, rather than a global, level - we often don't care as much about the full population's decisions as about the decisions made by friends and colleagues. For example, in a work setting we may choose technology to be compatible with the people we directly collaborate with, rather than the universally most popular technology. Similarly, we may adopt political views that are aligned with those of our friends, even if they are nationally in the minority.

Examples of Complex Contagion

• The credibility of an urban legend
  Urban legend
  An urban legend, urban myth, urban tale, or contemporary legend, is a form of modern folklore consisting of stories that may or may not have been believed by their tellers to be true...
  
  
• Willingness to participate in migration - (participating in a collective action)
• Incentives to exit formal gatherings
• What clothing to wear, hairstyle to adopt, and what part of the body to pierce

Gaming as a complex contagion : Argument: The act of gaming is a complex contagion; demonstrations, conventions, ongoing games, etc. are responsible for producing new gamers.