Allen Curve

Wikipedia: The Allen Curve is the "strong correlation between physical distance and the frequency of communication between work stations. The finding also revealed the critical distance of 50 meters for weekly technical communication."

Small World Phenomenon / Six Degrees

Wikipedia: "The small world phenomenon (also known as the small world effect) is the hypothesis that everyone in the world can be reached through a short chain of social acquaintances. The concept gave rise to the famous phrase six degrees of separation after a 1967 small world experiment by social psychologist Stanley Milgram which suggested that two random US citizens were connected by an average of a chain of six acquaintances."

Update:

Check out David Bradley's article on Six Degrees of Separation from ScienceBase and We’re Far Removed From Proof of ‘Six Degrees’ Theory from the Wall Street Journal.

Personal observation from Sean:

I have done work in this area [social network analysis] and have found that many of the "hubs" in organizations are so not because of titles, status or even friendliness but the result of physical location. For example, in a 300 person call center, the people with the most inbound links / edges tend to be those in the higher traffic areas.

Interestingly enough, most of the connections tend to cluster geographically where the average person relies on those in their immediate vicinity for the majority of information sharing: what we call "six feet of separation." Getting up to ask a question of someone outside of that immediate area presupposes the usually "good enough" answers available from their proximity peers may not be sufficient.

Weak Ties

Wikipedia: "Weak tie is a term suggested by Mark Granovetter in 'The strength of weak ties' (American Journal of Sociology, Vol. 78, No. 6., May 1973) as the ties in a social network that are not strong. Strong ties are those such as kin relations and close personal friends, while weak ties are loose acquaintances such as those connections made at a party."

Valids Krebs [via Twitter]: "That is NOT correct definition of weak tie -- college roommate who you rarely talk to is a weak tie -- there is trust in tie!"

Smart Mobs

Wikipedia: "The smart mob is a concept introduced by Howard Rheingold in his book Smart Mobs: The Next Social Revolution. According to Rheingold, smart mobs are an indication of the evolving communication technologies that will empower the people...

"A smart mob is a group that, contrary to the usual connotations of a mob, behaves intelligently or efficiently because of its exponentially increasing network links. This network enables people to connect to information and others, allowing a form of social coordination. Parallels are made to, for instance, slime moulds."

Valids Krebs [via Twitter]: "Two metrics necessary to determine 'small world': clustering coeff & avg path length, some use third metric of 'shortcuts'."

Social Capital

Wikipedia: "Social capital is defined by international intangible standards as the value that is created through the application of social networks during non-organizational time. From this stance, social capital when added to human capital summate to define economic capital."

Valids Krebs [via Twitter]: "strongest soc cap developed during project work -- thru work networks, not socializing -- thru tuff times, not good times.

Digg and Collective Intelligence

"Digg has a community of more than 600,000 registered users. They’ve gone far beyond the tipping point of creating a social networking site and some would argue they are spilling over with collective knowledge." /newassignment.net/

The Shifting Sands of Social Influence

"Scientists at the University of Massachusetts Dartmouth and the New England Complex Systems Institute have discovered that social networks and the roles of the individuals that make them up vary drastically from day to day. Until now, scientists have largely thought of networks as fairly stable, changing only slightly over time–say, when someone makes a new contact... When they looked at the e-mail traffic on any given day, they found that some people were hubs just as they expected. The surprise was that the identity of the hubs changed from day to day. " /smartmobs/

Preferential attachment

wikipedia: "In preferential attachment, new nodes are added to the network one by one. Each new node attaches itself (creates a link) to one of the existing nodes with a certain probability. This probability is biased, however, in the sense that it is proportional to the number of links that the existing node already has. Therefore, heavily linked nodes ('hubs') tend to quickly accumulate even more links, while nodes with only a few links are unlikely to be chosen as the destination for a new link. It is as if the new nodes have a 'preference' to attach themselves to the already heavily linked nodes...

"Preferential attachment is an example of a positive feedback cycle where initially random variations (one node initially having more links or having started accumulating links earlier than another) are automatically reinforced, thus greatly magnifying differences. This is also sometimes called the Matthew effect, 'the rich get richer', and in chemistry autocatalysis."

Scale-free network

wikipedia: "A scale-free network is a specific kind of complex network (in which) some nodes act as 'highly connected hubs' (high degree), although most nodes are of low degree."

Collective Intelligence

wikipedia: "One CI pioneer, George Pór, defined the collective intelligence phenomenon as 'the capacity of a human community to evolve toward higher order complexity thought, problem-solving and integration through collaboration and innovation.'"

Henry Jenkins: "In the classic formulation, collective intelligence refers to a situation where nobody knows everything, everyone knows something, and what any given member knows is accessible to any other member upon request on an ad hoc basis. Levy is arguing that a networked culture gives rise to new structures of power which stem from the ability of diverse groups of people to pool knowledge, collaborate through research, debate interpretations, and through such a collaborative process, refine their understanding of the world. If Koster is suggesting that the "wisdom of crowds" works badly when confronted with the challenges of politics in a democratic society, Levy sees "collective intelligence" as a vehicle for democratization, feeling that it provides a context through which diverse groups can join forces to work through problems."

Social Network Site

danah boyd: "a category of websites with profiles, semi-persistent public commentary on the profile, and a traversable publicly articulated social network displayed in relation to the profile."

Social Network Theory (SNT)

numb3rs blog: Applying Social Network Theory (SNT), related to social network analysis, "you can make up your own network diagrams that tell interesting stories of communication, isolation, rivalry and power. SNT is yet another example of an application of mathematical reasoning which is not restricted to simply manipulating numbers or geometric relationships. Rather, it is a creative combination of these and other elements to illuminate hidden relationships around us. For more on SNT, search the web. Here is a good starting site: How to do Social Network Analysis."

Stochastic

Wikipedia: "A stochastic process is one whose behavior is non-deterministic in that the next state of the environment is partially but not fully determined by the previous state of the environment."

Dictionary.com: "Involving or containing a random variable or variables"

Flock Theory

D. Rosen's blog: "Flock theory models the network evolution of human interaction via communication using a combination of self-organizing systems theory, network theory, and emergence theory. Flock theory may be viewed as an emergent theory of decentralized human interaction. The throng of collective action between flock members exemplifies the self-organizing ability of individuals that, despite their complexity, can demonstrate cooperative evolution. The coordinating ability of birds is viewed as an exemplar that is used to elucidate structure, while simultaneously establishing mechanisms of interaction that serve as a foundation for several constructs, and extended application to the small world phenomenon (i.e. six-degrees of separation)."

The Wisdom of Crowds

Wikipedia: "The Wisdom of Crowds: Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, Societies and Nations, first published in 2004, is a book written by James Surowiecki about the aggregation of information in groups, resulting in decisions that, he argues, are often better than could have been made by any single member of the group. The book presents numerous case studies and anecdotes to illustrate its argument, and touches on several fields, primarily economics and psychology."

Henry Jenkins summarizes Surowiecki's "contexts where his ideas about the wisdom of crowds apply:

"There are four key qualities that make a crowd smart. It needs to be diverse, so that people are bringing different pieces of information to the table. It needs to be decentralized, so that no one at the top is dictating the crowd's answer. It needs a way of summarizing people's opinions into one collective verdict. And the people in the crowd need to be independent, so that they pay attention mostly to their own information, and not worrying about what everyone around them thinks."

Cass Sunstein, author of the excellent Infotopia and Raph Koster qualifies the usefulness of the Wisdom of Crowds further: "Technically, Surowiecki’s conception of “wisdom of crowds” is ONLY applicable to quantifiable, objective data. The very loosey-goosey way of using it to discuss any sort of collective discussion and opinion generation is a misrepresentation of the actual (and very interesting) phenomenon.

"You can summarize the core phenomenon as 'given a large enough and varied population offering up their best estimates of quantity or probability, the average of all responses will be more accurate than any given individual response.' But this is of very narrow application — the examples are of things like guessing weight, market predictions, oddsmaking, and so on. The output of each individual must be in a form that can be averaged mathematically. What’s more, you cannot use it in cases where one person’s well-expressed opinion can sway another, as that introduces a subsequent bias into everything (which is why the wisdom of crowds doesn’t always work for identifying the best product on the market, or the best art, or the like)."

Reed's Law

Wikipedia: "Reed's law is the assertion of David P. Reed that the utility of large networks, particularly social networks, can scale exponentially with the size of the network.

"The reason for this is that the number of possible sub-groups of network participants is , where N is the number of participants. This grows much more rapidly than either the number of participants, N, or
the number of possible pair connections, (which follows Metcalfe's law)."

Metcalfe's Law

Wikipedia: "First formulated by Robert Metcalfe in regard to Ethernet, Metcalfe's law explains many of the network effects of communication technologies and networks such as the Internet and World Wide Web."

While Metcalfe's Law descrbes the potential value of a network (=N^2 where N is the number of network nodes), it likely overestimates the true value of a network (see Numb3rs blog for more details).

Network Effect

Wikipedia: "The network effect is a characteristic that causes a good or service to have a value to a potential customer dependent on the number of customers already owning that good or using that service.

"One consequence of a network effect is that the purchase of a good by one individual indirectly benefits others who own the good - for example by purchasing a telephone a person makes other telephones more useful. This type of side-effect in a transaction is known as an externality in economics, and externalities arising from network effects are known as network externalities. This is also an example of a positive feedback loop."

Diffusion of Innovations

Wikipedia: "The study of the diffusion of innovation is the study of how, why, and at what rate new ideas and technology spread through cultures."

Weak Signals

MGTylor.com: "Weak Signal Research refers to those organizational traits and organic components that enable the enterprise to detect weak signals as a matter of course, build models and stories that illustrate the possible effects of whole sets of signals over time, and redesign itself efficiently to take advantage of these possibilities."

Clustering Coefficient

Wikipedia: "Duncan J. Watts and Steven Strogatz (1998) introduced the clustering coefficient graph measure to determine whether or not a graph is a small-world network."

Dunbar Number: Rule of 150

Wikipedia: "The so-called rule of 150, states that the size of a genuine social network is limited to about 150 members (sometimes called the Dunbar Number). The rule arises from cross-cultural studies in sociology and especially anthropology of the maximum size of a village (in modern parlance most reasonably understood as an ecovillage). It is theorized in evolutionary psychology that the number may be some kind of limit of average human ability to recognize members and track emotional facts about all members of a group. However, it may be due to economics and the need to track 'free riders', as larger groups tend to more freely allow cheats and liars to prosper."

Social Network Analysis (SNA)

Wikipedia: "Social network analysis (also sometimes called network theory) has emerged as a key technique in modern sociology, anthropology, Social Psychology and organizational studies, as well as a popular topic of speculation and study. Research in a number of academic fields have demonstrated that social networks operate on many levels, from families up to the level of nations, and play a critical role in determining the way problems are solved, organizations are run, and the degree to which individuals succeed in achieving their goals."

IBM has a great article on social network analysis that is "first article in a series on collaboration, which is fast becoming recognized as an essential, yet often hidden, ingredient in working efficiently and effectively. This series focuses on tools and methods that can demystify collaboration and help IBM's clients harness its power."

For more info on the movement of ideas, influence and innovation through social networks, please visit patternhunter.com.

Also see Orgnet.com [Valdis Krebs' company] and Dr. Karen Stephenson for more information on professional Social Network Analysis.