Three Degrees of Influence is a theory in the realm of social networks,proposed by Nicholas A. Christakis and James H. Fowler in 2007. It has since been explored by scientists in numerous disciplines using diverse statistical, psychological, sociological, and biological approaches.
Christakis and Fowler explored the influence of social connections on behavior. They described how social influence does not end with the people to whom a person is directly connected. People influence their friends, who in turn influence their friends, and so on; hence, a person's beliefs and actions can influence people they have never met, to whom they are only indirectly tied. Christakis and Fowler posited that diverse phenomena "ripple through our network, having an impact on our friends (one degree), our friends’ friends (two degrees), and even our friends’ friends’ friends (three degrees). Our influence gradually dissipates and ceases to have a noticeable effect on people beyond the social frontier that lies at three degrees of separation." They posited a number of reasons for this decay, and they offered informational, psychological, and biological rationales.
This argument is basically that peer effects need not stop at one degree of separation. However, across a broad set of empirical settings, using both observational and experimental methods, they observed that the effect seems, in many cases, to no longer be meaningful at a social horizon of three degrees.
Using both observational and experimental methods, Christakis and Fowler examined phenomena from various domains, such as obesity, happiness, cooperation, voting, and various public health beliefs and behaviors. Investigations by other groups have subsequently explored many other phenomena in this way (including crime, social learning, etc.).
Influence dissipates after three degrees (to and from friends’ friends’ friends) for three reasons, Christakis and Fowler propose:
Initial studies using observational data by Christakis and Fowler suggested that a variety of attributes (like obesity,smoking, and happiness ), rather than being individualistic, are casually correlated by contagion mechanisms that transmit such phenomena over long distances within social networks. Certain subsequent analyses have explored limitations to these analyses (subject to different statistical assumptions); or have expressed concern that the statistical methods employed in these analyses cannot fully control for other environmental factors; or have noted that the statistical estimates arising from some approaches may not always have straightforward interpretations; or have argued that the statistical methods may not always account for homophily processes in the creation and retention of relationships over time.
But other scholarship using sensitivity analysis has found that the basic estimates regarding the transmissibility of obesity and smoking cessation, for example, are quite robust,or has otherwise replicated or supported the findings. Additional, detailed modeling work published in 2016 showed that the GEE modeling approach used by Christakis and Fowler (and others) was quite effective for estimating social contagion effects and in distinguishing them from homophily. This paper concluded, "For network influence, we find that the approach appears to have excellent sensitivity, and quite good specificity with regard to distinguishing the presence or absence of such a 'network effect,' regardless of whether or not homophily is present in network formation. This was true for small cohorts (n = 30) and larger cohorts (n = 1000), and for cohorts that displayed lesser and greater realism in their distribution of friendships." Another methodological paper concluded that it is indeed possible to bound estimates of peer effects even given the modeling constraints faced by Christakis and Fowler —even if parametric assumptions are otherwise required to identify such effects using observational data (if substantial unobserved homophily is thought to be present).
Additional support for the modeling approach used by Christakis and Fowler provided by other authors has continued to appear.From a theoretical perspective, it has been shown that this property naturally emerges as the outcome of the interplay between social influence, or learning dynamics, and complex networks. These studies employ emblematic models used to study the diffusion of information, opinions, ideas and behaviors on a wide range of network topologies, showing also under which conditions violations of the "three degrees of influence” can be expected including of the three-degrees-of-influence property. Additional analytic approaches to observational data have also been supportive, including matched sample estimation, and reshuffling techniques. The reshuffling technique validated the "edge directionality test" as an identification strategy for causal peer effects; this technique was first proposed by Christakis and Fowler as a tool for estimating such effects in network analysis in their 2007 obesity paper.
Christakis and Fowler reviewed critical and supportive findings regarding the three degrees of influence phenomenon and the analytic approaches used to discern it with observational data in 2013.
In addition, subsequent experimental studies (by many research groups, including Christakis and Fowler) have found strong causal evidence of behavioral contagion processes that spread beyond dyads (including out to two, three, or four degrees of separation) using randomized controlled experiments,including one experiment involving 61,000,000 people that showed spread of voting behavior out to two degrees of separation. A 2014 paper also confirmed the spread of emotions beyond dyads, as proposed in 2008 by Christakis and Fowler, using another massive online experiment. The "three degrees of influence" property has also been noted by other groups using observational data regarding criminal networks.
Diverse lines of work have also explored the specific biopsychosocial mechanisms for the boundedness of contagion effects, some of which had been theorized by Christakis and Fowler. Experiments by Moussaid et al. evaluated the spread of risk perception, and documented inflection at approximately three degrees.Another set of experiments documented the impact of information distortion, noting that "despite strong social influence within pairs of individuals, the reach of judgment propagation across a chain rarely exceeded a social distance of three to four degrees of separation.... We show that information distortion and the overweighting of other people’s errors are two individual-level mechanisms hindering judgment propagation at the scale of the chain." And experiments with fMRI scans in a sociocentrically mapped network of graduate students, published in 2018, showed that neural responses to conceptual stimuli were similar between friends, with a nadir at three degrees of separation, providing further biological evidence for this theory.
The theory has also been used to develop validated algorithms for efficient influence maximization.
The idea of network influence raises the question of free will, because it suggests that people are influenced by factors which they cannot control and which they are not aware of. Christakis and Fowler claim in their book, Connected, that policy makers should use knowledge about social network effects in order to create a better society with a more efficient public policy. This applies to many aspects of life, from public health to economics. For instance, when resources are scarce, they note that it might be preferable to immunize individuals located in the center of a network in preference to structurally peripheral individuals. Or, it might be much more effective to motivate clusters of people to avoid criminal behavior than to act upon individuals or than to punish each criminal separately. Their subsequent work has explored how to use social contagion to foster the spread of desirable innovations in rural villages.
Duncan James Watts is a sociologist and a Professor at the University of Pennsylvania. He was formerly a principal researcher at Microsoft Research in New York City, and is known for his work on small-world networks.
Social influence comprises the ways in which individuals change their behavior to meet the demands of a social environment. It takes many forms and can be seen in conformity, socialization, peer pressure, obedience, leadership, persuasion, sales, and marketing. Typically social influence results from a specific action, command, or request, but people also alter their attitudes and behaviors in response to what they perceive others might do or think. In 1958, Harvard psychologist Herbert Kelman identified three broad varieties of social influence.
Homophily is a concept in sociology describing the tendency of individuals to associate and bond with similar others, as in the proverb "birds of a feather flock together". The presence of homophily has been discovered in a vast array of network studies: over 100 studies have observed homophily in some form or another, and they establish that similarity is associated with connection. The categories on which homophily occurs include age, gender, class, and organizational role.
A small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely to be neighbors of each other and most nodes can be reached from every other node by a small number of hops or steps. Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes grows proportionally to the logarithm of the number of nodes N in the network, that is:
Emotional contagion is a form of social contagion involving the spontaneous spread of emotions and related behaviors. Such emotional convergence can happen from one person to another, or in a larger group. Emotions can be shared across individuals in many different ways both implicitly or explicitly. For instance, conscious reasoning, analysis and imagination have all been found to contribute to the phenomenon. The behaviour has been found in humans, other primates, dogs, and chickens.
In the study of complex networks, assortative mixing, or assortativity, is a bias in favor of connections between network nodes with similar characteristics. In the specific case of social networks, assortative mixing is also known as homophily. The rarer disassortative mixing is a bias in favor of connections between dissimilar nodes.
A web-based experiment or Internet-based experiment is an experiment that is conducted over the Internet. In such experiments, the Internet is either "a medium through which to target larger and more diverse samples with reduced administrative and financial costs" or "a field of social science research in its own right." Psychology and Internet studies are probably the disciplines that have used these experiments most widely, although a range of other disciplines including political science and economics also use web-based experiments. Within psychology most web-based experiments are conducted in the areas of cognitive psychology and social psychology. This form of experimental setup has become increasingly popular because researchers can cheaply collect large amounts of data from a wider range of locations and people. A web-based experiment is a type of online research method. Web based experiments have become significantly more widespread since the COVID-19 pandemic, as researchers have been unable to conduct lab-based experiments.
James H. Fowler is an American social scientist specializing in social networks, cooperation, political participation, and genopolitics. He is currently Professor of Medical Genetics in the School of Medicine and Professor of Political Science in the Division of Social Science at the University of California, San Diego. He was named a 2010 Fellow of the John Simon Guggenheim Foundation.
Social network analysis software is software which facilitates quantitative or qualitative analysis of social networks, by describing features of a network either through numerical or visual representation.
An ecological network is a representation of the biotic interactions in an ecosystem, in which species (nodes) are connected by pairwise interactions (links). These interactions can be trophic or symbiotic. Ecological networks are used to describe and compare the structures of real ecosystems, while network models are used to investigate the effects of network structure on properties such as ecosystem stability.
Behavioral contagion is a form of social contagion involving the spread of behaviour through a group. It refers to the propensity for a person to copy a certain behavior of others who are either in the vicinity, or whom they have been exposed to. The term was originally used by Gustave Le Bon in his 1895 work The Crowd: A Study of the Popular Mind to explain undesirable aspects of behavior of people in crowds. In the digital age, behavioural contagion is also concerned with the spread of online behaviour and information. A variety of behavioral contagion mechanisms were incorporated in models of collective human behavior.
Nicholas A. Christakis is a Greek-American sociologist and physician known for his research on social networks and on the socioeconomic, biosocial, and evolutionary determinants of behavior, health, and longevity. He is the Sterling Professor of Social and Natural Science at Yale University, where he directs the Human Nature Lab. He is also the Co-Director of the Yale Institute for Network Science.
The friendship paradox is the phenomenon first observed by the sociologist Scott L. Feld in 1991 that most people have fewer friends than their friends have, on average. It can be explained as a form of sampling bias in which people with more friends are more likely to be in one's own friend group. Or, said another way, one is less likely to be friends with someone who has very few friends. In contradiction to this, most people believe that they have more friends than their friends have.
Social contagion involves behaviour, emotions, or conditions spreading spontaneously through a group or network. The phenomenon has been discussed by social scientists since the late 19th century, although much work on the subject was based on unclear or even contradictory conceptions of what social contagion is, so exact definitions vary. Some scholars include the unplanned spread of ideas through a population as social contagion, though others prefer to class that as memetics. Generally social contagion is understood to be separate from the collective behaviour which results from a direct attempt to exert social influence.
The Matthew effect of accumulated advantage, Matthew principle, or Matthew effect for short, is sometimes summarized by the adage "the rich get richer and the poor get poorer". The concept is applicable to matters of fame or status, but may also be applied literally to cumulative advantage of economic capital. In the beginning, Matthew effects were primarily focused on the inequality in the way scientists were recognized for their work. However, Norman W. Storer, of Columbia University, led a new wave of research. He believed he discovered that the inequality that existed in the social sciences also existed in other institutions.
In graph theory, betweenness centrality is a measure of centrality in a graph based on shortest paths. For every pair of vertices in a connected graph, there exists at least one shortest path between the vertices such that either the number of edges that the path passes through or the sum of the weights of the edges is minimized. The betweenness centrality for each vertex is the number of these shortest paths that pass through the vertex.
In mathematical modeling of social networks, link-centric preferential attachment is a node's propensity to re-establish links to nodes it has previously been in contact with in time-varying networks. This preferential attachment model relies on nodes keeping memory of previous neighbors up to the current time.
Global cascades models are a class of models aiming to model large and rare cascades that are triggered by exogenous perturbations which are relatively small compared with the size of the system. The phenomenon occurs ubiquitously in various systems, like information cascades in social systems, stock market crashes in economic systems, and cascading failure in physics infrastructure networks. The models capture some essential properties of such phenomenon.
Targeted immunization strategies are approaches designed to increase the immunization level of populations and decrease the chances of epidemic outbreaks. Though often in regards to use in healthcare practices and the administration of vaccines to prevent biological epidemic outbreaks, these strategies refer in general to immunization schemes in complex networks, biological, social or artificial in nature. Identification of at-risk groups and individuals with higher odds of spreading the disease often plays an important role in these strategies.
Damon Centola is a sociologist and professor in the Annenberg School for Communication, the School of Engineering and Applied Sciences, and the Department of Sociology in the School of Arts and Sciences at the University of Pennsylvania, where he is director of the Network Dynamics Group. Previously, he was an assistant professor at M.I.T. Sloan School of Management (2008–2013). He was also a Robert Wood Johnson Fellow at Harvard University, a member of Sci Foo Campers community, and a fellow of the Center for Advanced Study in the Behavioral Sciences at Stanford University.