At the beginning of the semester we were given a sheet depicting numerous real life models of a variety of social networks. Most of edges concerned interaction between nodes, such as the spread of informational e-mails, friendships within organizations and clubs, or the outbreak of a disease. This blog focuses on a more theoretical application of both game theory and network dynamics.

Experts connected to the Brookings Institute have developed a theoretical “simulation” centered on the dynamics of the spread of fear and disease in a paper entitled, “Coupled Contagion Dynamics of Fear and Disease: Mathematical and Computational Explorations,” by Joshua M. Epstein, Jon Parker, Derek Cummings, and Ross A. Hammond

(http://www.brookings.edu/~/media/Files/rc/papers/2007/10dynamics_epstein/10dynamics_epstein.pdf).

The first part of the paper describes a model in which (1) a disease is spread throughout a population in concert with (2) the fear of contracting that disease. Traditional mathematical epidemiology models assume perfect mixing within the population. In contrast, these authors model a population in which people, when confronted with the fear of contracting a disease, may change their social patterns or “contact patterns”. Both fear and the disease itself are similarly contagious in their model and both can spread independently. Disease is spread through contact with the disease-infected, while fear is spread through contact with disease-infected, fear-infected, or disease-and-fear-infected people. People within the network fall into seven categories (Susceptible to pathogen and fear, Infected with fear only, Infected with pathogen only, Infected with pathogen and fear, Removed from circulation due to fear, Removed from circulation due to fear and infected with pathogen, Recovered from pathogen and immune to fear).

A key conclusion from the model is that fear spreads faster than disease. While disease can spread through people infected with the pathogen or infected with the pathogen and fear, fear can spread in three ways: people the have contracted the infection, contracted fear, or contracted fear and the infection. A second conclusion emerges when the authors consider flight due to fear of disease: flight amplifies the spread of diseases. That is, the barrier between the infected and those susceptible to infection is broken with the flight of fearful individuals. The authors reference several cases in support of their elegant model.

Several interesting expansions of this model come immediately to mind. Consider, for example, overlaying this model with the additional variable of level and sophistication of communication. With limited communication, i.e., in the pre-information boom era with the internet and television, the original model would have held. An example that comes to mind is spread of disease brought by Europeans to the Americas in the 15th and 16th centuries. As more people fled the disease, this would have had a predictably amplified effect on the population. But now consider a similar situation in the presence of nearly perfect information transfer and exchange. While one may see a similar change in social patterns, would the same “flight” instinct hold in an informed population? Take for instance the spread of meningtis throughout a population. A highly contagious disease, a case of meningitis has the potential to spread rapidly, and amplified as people fled the disease. In a hypothetical population lacking near perfect information, one may see a similar pattern of flight as a result of fear from the disease. Today though an outbreak of menigitis means nothing more than shots for the networks of infected individuals, individuals infected with fear, and those infected with both fear and the disease. Moreover though it may be the instant spread of information between well informed individuals that dampens the “flight” tendency? Something for thought.

http://money.cnn.com/news/newsfeeds/articles/newstex/IBD-0001-22942744.htm

On February 1, Microsoft offered $44.6 billion deal to Yahoo. While reading some of the articles, it was interesting to find out that many articles described MS-Yahoo deal as a game. Some articles, including the one linked above, referred to the specific type of a game called the chicken game, another name for Hawk-Dove game. Although the meaning of a game used in articles is not exactly same as the term used in game theoretic methods, applying the definition of a game discussed in the class would be useful analyzing MS-Yahoo deal.

Applying the definition of a game, this deal can be analyzed as a game played by 2 players, MS and Yahoo, with set of strategies and payoffs. For Yahoo, set of strategies could be simply accepting or rejecting the offer or it could be more complicated such as five possible scenarios analyzed by Mark Mahaney, an analyst with Citigroup. (http://blogs.barrons.com/techtraderdaily/2008/02/05/yahoo-the-five-scenario-analysis/) Players can determine payoffs by analyzing relevant numbers such as market share and revenue. (http://www.zdnet.com.au/news/business/soa/Microsoft-Yahoo-deal-Playing-the-numbers-game/0,139023166,339285649,00.htm)

Yahoo rejected Microsoft’s offer on February 11. In addition, Yahoo began talks with Google, News Corporation, and Time Warner; however, the game is not over. The game is changing overtime as one player reveals its own best strategy with respect to other player’s set of strategies by adding new strategy to the game. Also additional players may influence the game when Google and Time Warner try to participate in the game.

For each player, it is important to have a clear understanding of possible set of strategies and payoffs so that each can choose the best response. According to the email from Jerry Yang, CEO of Yahoo, to Yahoo employees, what they are trying to do is to discover the set of strategies available to them, “our board is thoughtfully evaluating a wide range of potential strategic alternative” (http://www.sec.gov/Archives/edgar/data/1011006/000095013408001763/f37757exv99w1.htm) It is important to not only analyze and choose among given strategies, but to develop new ones.

https://www.timesonline.co.uk/tol/comment/columnists/daniel_finkelstein/article3399671.ece

http://findarticales.com/p/articles/mi_m1200/is_4_166/ai_n6151880/

In a recent article on the timesonline.co.uk website, game theory was related to the politics in relations to the Tories. In the article,game theory’s selfish strategies and cooperative strategies are discussed and an interesting point about vampire bats were mentioned. Upon some searching, I came across and article in Science News further explaining the example of the vampire bats.

Given a successful night of hunting, a vampire bat would often share the blood that it had gathered throughout the night with other bats that had not had a successful night of hunting. Taking each bat as players in the game of survival, such actions are not the ones predicted through game theory modeled by the prisoner’s dilemma. For a bat, hoarding the excess blood and surviving well after the other bats logically would be the goal. The reward for obtaining this goal is the opportunity to further reproduce and to pass their own genes to their off-spring. However, as this article discusses, due to evolution and lessons learned from previous generations of bats, the bats shares the excess blood would benefit the colony as a whole and in essence allows for others to benefit as well.

The article also discusses the prisoner’s dilemma but further mentions that it is an insufficient model for this specific case since it focuses on the self-preservation motivated strategies. A different strategy, the cooperation strategy such as our hawk-dove game, is modeled by two cars stuck in a snowdrift. Without going into details of this game, the outcome shows that the decisions of each player will depend heavily on the decision made by the other. For example, given that two cars are stuck in the same mound of snow, each has the options of shoveling the snow or sitting in their cars. In this case, if both players see that the other is sitting in, they no longer have the option to sit in because then no snow would be moved. Thus, both players will end up cooperating and in essence sacrifice their own comfort to benefit the group.

Between two players, fairness, to the rational person, is seen is a 50:50 split. To illustrate an example let’s say there’s Kenny and Roger and these two players are to split $100 between themselves. Kenny has the task of proposing an amount and Roger can either accept or reject his offer. Now let’s say Kenny initially proposes a 90:10 split. Obviously, Roger will reject the offer since he’s aware of the unbalance of the situation and would prefer a sum of $0 rather than see Kenny get $90. The only instance in which Roger will accept Kenny’s proposal is if there is a fair distribution of money between them (i.e., 50:50). This example illustrates the Ultimatum Game.

Evolution and the Ultimatum Game, presents evidence of this same fair behavior among other animals. Two studies have shown that chimpanzees and monkeys display similar behavior.

In one study, chimpanzees were given raisins to split among each other. As in the Kenny and Roger example, one chimpanzee would make the split and the other would accept or reject the offer. Results showed that given any positive split, the chimpanzees would not reject an offer. However, the only time a chimpanzee would reject was when the responder was not given any raisins.

In a more detailed study found on the National Geographic site, Monkeys Show Sense Of Fairness, Study Says, researchers at Emory University used the concept of the Ultimatum Game on capuchin monkeys, a highly social species.

These monkeys were trained to retrieve a pebble and in return would be awarded a cucumber. Once the monkeys equated a pebble with a cucumber, the researchers paired them in teams. On occasion, after retrieving a pebble one monkey would receive a cucumber while the partner received a grape. Later on, some monkeys would receive a cucumber or grape for doing nothing at all. The continuation of these ‘unfair’ trades led to visible discontent in those monkeys who were continually given the short end of the stick. The results lead us to believe that these capuchin monkeys exhibit the notion of fairness and thusly follow the Ultimatum Game.

Lately in class, we have been discussing the evolution of information networks. With the creation of these networks, we have all benefited from rapid search, aggregation of data from diverse sources, and presentation of data based on ratings of relevance. With such speedy access and facilitation of information flow, how could these information networks ever create a disservice to individuals such as you and me? Well, consider a concept addressed in the earlier part of our classes as well as a fairly recent post: structural holes. As posited by Burt, the benefit of spanning a structural hole was the “gatekeeping” role, the ability to restrict the flow of information from one component to the next. Now consider how such “gatekeeping” could exist in an information network. With the rapid aggregation of sources and the more permanent structure of information in the digital context, the individual web user has very little control over the flow of information throughout the network. The main question that arises is: are all forms of structural holes obliterated with the creation of the internet? The working research by Danah Boyd, Jeff Potter, and Fernanda Viegas shows that though the internet has weakened an individual’s ability to maintain structural holes, we have created unique identity preservation methods to maintain structural holes in the social context.

Burt specifically speaks about the benefits of structural holes in the industrial, organizational context. As further discussed in class, those who span structural holes have the 3 following advantages:

1)Informational: early access to non interacting parts of the network

2)Creativity amplifier: those bridging structural holes can create novel solutions by combining information from various sources

3) Gate keeping: those who span structural holes can decide if nodes in one component can receive information from nodes to another component.

So in the business context, it appears that those spanning structural holes benefit from their controlling position. However, a Bearman-Moody study found that structural holes in the social context may be detrimental. With very little embededness and congeniality among friends, those spanning structural holes are exposed to variety of norms. Such a lack of a tightly-knit social support system could cause undue stress on the individual. Though the Bearman-Moody study confirms the notion that structural holes may be detrimental in the social context, there are many ways that we create beneficial structural holes in the formation of our identity. Boyd, Potter, and Viegas discuss the role of structural holes in social identity formation. The authors proffer that we have two sets of identities that interact and help form the other. However, the basis for each identity is distinct. First, we have a personal identity, formed from our innermost thoughts and values. Second, we have a social identity that we form from the various network contexts we are in. For example, the person I portray to a group of friends is very different from the person I portray to my family, professors, or coworkers. It is such a bifurcation of self where structural holes play an integral part in maintaining harmony among our many social identities. For example, it would be very troublesome (to me at least) if I ran into the interviewer for a summer internship while I was in a less decorous state at a local hotspot.

So even though structural holes may be detrimental by exposing us to a variety of norms that we may find hard to balance, they offer benefits by allowing us to maintain various social identities. Maintaining such separation is relatively easy in the physical world. There are many mechanisms to maintain structural holes such as physical separation or temporal separation. Furthermore, there is a mutability aspect of information shared with those in physical networks. The ability for information to pass from one component to the other depends on the level of separation of the components as well as the particular nodes even remembering the shared personal information. However, in the digital context, geographical separation is not a factor and there is a level of immutability of information shared. With the millions of archives that can be accessed through just one link, fortuitous “forgetting” by nodes is not as prevalent among a digital network. Furthermore, multiple corporations have devised methods of detecting exactly who we are through cookies and emerging software to identify individuals by patterns of speech. Though it may appear that maintaining control over a distinct and private identity is impossible in the digital network, the authors’ intensive review of a 5 year email record of “Mike” proves that we have created clever means to maintain a distinct identity among our social cohorts.

figure 1: example of “Mike’s” structural holes in email accounts 

The first simple method of maintaining structural holes in the information age is to send different messages to different groups under a different email alias. For example, let’s say I want to invite my family, friends, and possible employers to a mixer I am having. I will first write three distinct messages: one with a sentimental and loving tone for family, one with a naughty tone for friends, and one with a formal tone to possible employers. However, a possible problem is that my brother might interact with my friend in a chatroom. He might notice my email alias on her list of friends and somehow gains access to my naughty message. In this case, the bridging mechanism of the internet has beaten my attempts to maintain structural holes and has created a bridge, eliminating my control over my bifurcated personality. I might combat this phenomenon by creating multiple email aliases for each component.

In their paper, the authors propose that we maintain structural holes by our email strategies. In terms of game theory, it is our dominant strategy to maintain a different self for every network and context. No matter what other nodes do, our ability to adapt to situations will expose us to a variety of networks thus conferring informational and social advantages. The gist of the author’s argument is that we establish trust and maintain our different personas through email functions such as the carbon copy and blind carbon copy. The three ties according to the article are knowledge ties, awareness ties and trusted ties defined as follows:

Knowledge ties: If A sends a message to B, then we assume that A knows B but not necessarily that B knows A. (This is a good example of the directional edges seen in many link connections in informational networks)

Awareness ties: If B receives a message from A, then B is “aware” of A. Furthermore, if B and C receive a message from A then B and C are aware of each other. In this example, B and C would most likely be two nodes from the same component. It would not be detrimental to A if B and C somehow contacted each other without A present

Trust ties: If A sends and message to B and Blind Carbon Copies the message to C, then we assume that A “knows” and “trusts” C. This assumption makes sense because C has the ability to respond and reveal to B that A sent a message to others without his awareness.

The working paper goes through an example of Mike’s email to a group of friends to illustrate the difference between knowledge, awareness, and trust ties. However, the main take-away message from the paper is that even though digital contexts have limited our ability to maintain structural holes, we have found methods to subvert complete access to ourselves and have been able to maintain many social selves.

Figure 2: Mike’s many different social selves Blue: friends Brown: School Pink: work Green: Website, images retrieved from powerpoint presentation link to presentation:http://smg.media.mit.edu/projects/SocialNetworkFragments/presentation/sunbelt.ppt

The article and accompanying slide presentation on the site offer a unique integration of concepts addressed at different periods of our instruction. We see how the digital world has hindered our ability to maintain structural holes, but that we have created novel methods to adjust to such restraints. This work illustrates one of the key concepts of network analysis: a network is the sum of our interactions which we in turn react to.

An interesting topic that the article addressed that is similar to concepts in class, but not directly discussed in class was that of “Simmelian ties” proposed by Krackhardt. According to Krackhardt, and individual is Simmelian tied to another if 1) they share a strong tie with one another and 2) if they share a strong tie with at least one other person. Such a concept brings strong triadic closure to a whole other level. Now, rather than the formulation of a weak or strong tie, under Simmelian ties, a clique must consist of at least a triangle with all strong ties.

Simmelian ties and “Mike’s” digital identity formation are more exhaustively described by

Danah Boyd, Jeff Potter and Fernanda Viegas in their working paper:

Fragmentation of identity through structural holes in email contacts.

Link to Site http://smg.media.mit.edu/projects/SocialNetworkFragments/presentation/index.html

Link to paper:http://smg.media.mit.edu/projects/SocialNetworkFragments/presentation/HalfPaper.pdf

On the Thursday evening when I should have been working on “Networks” Homework #3 I escaped with my wife to a performance at Ithaca College of “La Finta Giardiniera”, a comic opera written by Mozart when he was 18 years old.  But there in the program for the performance I found “Notes from the Director” consisting solely of the following network diagram (included here with permission of the director, David Lefkowich):

Remarkably, this diagram summarizes a good part of the silly, fun plot, with the rest built around disguised identities, characters milling around in the dark, and unclear romantic allegiances, all staged by the director in an updated, “Sopranos” style.   As I watched the action unfold and listened to Mozart’s glorious music, I wondered idly whether the network exchange theory we learned in “Networks” could help predict the outcome of the plot.

Looking closely at the network, we see seven character nodes, connected by edges, some of which have hearts, broken or whole, along them.   Along with the edges that represent romantic ties are two that are about other relationships:  Arminda as Podesta’s niece and Nardo/Roberto as Violante/Sandrina’s servant.  An edge from Belfiore to Violante says “STABBED!” since before the action of the play, Belfiore had stabbed Violante in a jealous fit, and left her for dead.   Eliminating these edges, the hearts, and the arrowheads  yields a simple linear network of a form that should be familiar to students of “Networks” (with dashes representing the edges):

Following the analytical approach used in the course, we see that Nardo and Ramiro have little power since they have no outside alternatives.   Serpetta and Arminda have more power, Podesta and Belfiore less than the two of them, and Violante the most power moreover the opera is named after her, since she is La Finta Giardiniera [the pretend lady gardener].*    Violante can chose between Podesta, the ‘godfather’ or governor of the Black Sea town where the play takes place, and  Belfiore, whom she loved but who ran away after jealously wounding her and has now shown up in the town where Violante is working as a gardener.  If she chooses Podesta, Arminda is free to proceed with her marriage to Belfiore or to respond to Ramiro’s love for her and  Nardo is free to wed Serpetta if she will have him.   If Violante chooses Belfiore,  Podesta may respond to Serpetta’s attraction to him or Serpetta may accept Nardo’s attentions, while Ramiro is free to pursue Armindo.  

Redrawing the network as a bipartite graph, with the women on the left and the men on the right, reveals another construct studied in “Networks”:

Not only is this a bipartite graph, but it has a constricted set — there are four men and only three women, so there cannot be a perfect matching.   In order to permit a perfect matching, we must add an artificial node, representing bachelorhood or a fourth woman. 

 However the economic approach developed in “Networks” to handle this kind of network is insufficient to explain which of the possible perfect matchings ensues (as it should be!).  This is largely because the model is incomplete in at least two ways.  It does not take into account class structure: Serpetta and Nardo are both servants and so in the original era of the play seem more likely to end up together,  while Belfiore is a Count, Violante a Countess, and Podesta a mere politician (who, like Tony Soprano, thinks he controls more than he does).    Moreover by leaving out the arrowheads our simplification of the network has eliminated the directed nature of some of the edges as well as the heart labels, broken or whole, all of which  represent the past and present emotional ties.**

Here is where the 18-year-old Mozart, who did not write the story (which is attributed to Petrosellini) but who uses music in his operas to reveal character and relationships, comes to our aid.   Much of the opera consists of negotiations among the participants, working out which exchanges will occur, though unlike the experiments described in the course these are in the form of arias, duets and even ensembles, not Instant Messanger sessions. Thus the climax of the story occurs in  the beautiful duet “Tu mi lasci?” [are you leaving me?],  in which Belfiore and Violante are drawn together again all the while protesting that they are leaving each other, accompanied by orchestral music that clearly urges reconciliation and union.

And so the opera ends with a “perfect matching”:

VIOLANTE/SANDRINA—–BELFIORE 

NARDO/ROBERTO—–SERPETTA

 ARMINDA—–RAMIRO

But  what of Podesta?  Well, he sings  ”Ch’io pur mi sposero, Quando un’altra Sandrina trovero” [as for me, I will marry when I find another Sandrina], reconciling himself to having to match to the artificial  node after blessing the other three matches. 

What if Mozart, like the Ithaca College production, were transported to contemporary times and like me, is auditing ”Networks”?   Like me, he might well have had a lot of fun working out this network analysis of his opera without taking the analytical approach any more seriously than he has taken the plot.  

 (Here is a full summary of the plot of La Finta Gardiniera).

 *Professor Kleinberg confirms that this analysis is consistent with experimental results on seven node linear networks, but says that the only stable outcome would give Serpetta, Violanta and Arminda each one and everyone else zero.   (Sorry, guys….)  

** Professor Kleinberg says he does not know of any extension of network exchange theory to directed graphs, but asks what such a model might capture.   I would guess that if A is in love with B but B does not (yet) reciprocate, A is at a power disadvantage with respect to B, while if the edge between C and D is bidirectional together they have power greater than one.    

Co-Authorship Networks in the Digital Library Research Community presents an investigation on the DL research community based on examination of the co-authorship network of 1567 authors, based upon papers submitted to three DL conferences from 1995 to 2003.

The research team experimented with a number of metrics intended to characterize the network, which are detailed in the paper. The group concluded that the co-authorship network demonstrated a relatively high degree of clustering with smaller components; that is, it seems apparent that the DL research community is significantly more disperse than other research communities.

This would seem to indicate that the research community might contain several structural holes. The figure below represents a clustering applied to authors within the network, using a distance metric based on inter-authorship similarity. The smallest clusters formed within the institutions shown at the first level of the clustering. Based on what we discussed in class, one would then expect the authors connecting clusters to be, in a sense, more powerful.

This is indeed the case. Consider the following example: the authors from LANL, Cornell, and Southampton form a first level cluster. Carl Lagoze, a researcher here at Cornell, has been at the forefront of collaborative projects with each institution (the Open Archives Initiative with LANL and the Open Citation Project with Southampton). Furthermore, Lagoze is ranked very highly by several of the group’s measures of author importance. It seems reasonable to attribute this status due to his position within the co-authorship network.

            In his efforts to objectively settle debates about athletic prowess, one blogger has developed statistical similarity networks for NBA players and Major League Baseball batters.  By finding each player’s ratio for all statistical categories (e.g. Free-throw Percentage/Turnovers per game), then normalizing the results in each category, the author found the Euclidian distance between each pair of players.  In resulting network, the nodes represent individual players and their career statistical set, while, and edges directed edges connect any player to the player whose competitive output is most similar (the least sum of squared differences between their statistical ratios). 

The info network graphs visually display components of similarly effective players.  Some of the results are quite intuitive, such as the proximity between steroid-linked power hitters like Barry Bonds, Jose Canseco and Gary Shefield.  However, this method also helps uncover pairings such as Joe Carter and Nomar Garciapara, whose different positions, size and race make them a non-obvious statistical duo that subjective analysis would probably overlook. 

            This methodology provides a compelling approach to verify claims of similarity and to discover new matches.  One could extend the system to comparing non-individual actors such as universities, sports teams or even national/regional economies.  If combined with time-series analyses, this type of info network could also illuminate the development of certain types of components or “authorities,” nodes with a concentration of inward connections, which represent the leaders or most-

emulated actors in a given field.

http://www.nytimes.com/2008/03/05/business/smallbusiness/05edge.html

In the article “Storing Information for Profit” by the New York Times, a new technological development called “cloud computing” shows promise in permanently altering the corporate and information network structures of our world. The emergence of cloud computing in the corporate environment offers companies “information that is stored on the World Wide Web and not in a single company’s operating or applications systems.” Technological firms such as Google and IBM are already developing technology to centralize corporate data into one aggregate server. This provides a cost-efficient alternative to the cost of individual firms developing IT by essentially outsourcing this function to a middleman such as BPO Management Services of Anaheim, California and “[relieving] a small business of the need to maintain and constantly upgrade information systems”. In addition, some companies such as Docstoc.com are taking cloud computing to the next level: by aggregating “samples of business and legal documents, including business plans, employment forms, noncompete contracts, living trusts and so forth” into an easily accessible pool of information. Access to this information can greatly enhance the consulting and referral capabilities of a company such as Docstoc.com and prove it to a valuable asset to a small to middle-sized business struggling to maximize the power of IT.

Computer industry experts such as Patrick Dolan, founder of BPO, consider

“Web-based commerce, which depends on powerful centers of computing power, recalls an old concept, “that the computing industry would evolve as the electrical industry did, with central power plants” feeding remote distribution outlets.”

Through their power to accumulate data from various businesses and organizations, cloud computing companies capitalize on creating “local bridges”. Businesses that seek information management companies such as BPO are essentially creating an edge with a local bridge. This edge offers a small business something it cannot gain from any of its other edges: access to a new, previously inaccessible component of the corporate network, that is all the subcomponents of companies that have used an information management group such as BPO. The new local bridge that forms opens up the small business to a vast source of innovative ideas and alternative perspectives. New opportunities may arise that never have come to surface had there not been this edge.

However, cloud computing, although holding the potential to greatly accelerate societal development, can cause great imbalances of power in a network system. Because of the multiple local bridges that form with a company such as BPO, BPO can potentially hold great power in the corporate network. By covering many structural holes in the corporate network, BPO controls access between many different nodes (businesses and their data). Thus, small businesses should exercise great caution when entrusting their firm’s information to an information management group, which like all other companies in the capitalist USA is still driven by the incentive of profits.

Who Rises to Power in American Business?

Please find summarized here the above-linked Question and Answer with Anthony J. Mayo, co-author of the book

Paths to Power: How Insiders and Outsiders Shaped American Business Leadership

.

The book itself, which came out in January 2007, is “the first book in fifty years to exhaustively analyze the demographics of leadership and access in business in the U.S.” An excerpt may be found at the bottom of the page, which mentions many different networking means available to prospective business leaders in the past century, some of which include marriage, scholarly fellowship, joint military service, and political involvement.

One of the conclusions of Mayo et al. is that the success of early 20th Century business leaders was primarily based upon the right connections of religion, family, class status, geographic location, and education. These “insiders” would be comparable to nodes of high clustering coefficients that we saw in our discussions of Network Structure, Weak Ties, and Triadic Closure. On the other hand there did exist “outsiders” (in terms of the criteria above) who managed with some lesser frequency to achieve great success. These individuals may be seen as spanning structural holes through their connections back to the “outsider” community.

Another comment made on the success of young entrepreneurs was the importance of an initial powerful benefactor to grace the start-up with some positive reputation and opportunities. In other words, this benefactor would provide triadic closure between the young entrepreneur and potential customers, as well as adding the assurance accorded by raising the embeddedness of the edge representing the fledgling deal. To quote Mayo on this phenomenon, “In a sense, this personal network or connection helped to facilitate access to others in positions of influence which in turn provided opportunities for advancement.”

Other methods of fostering connections with an aim to achieving business prominence included getting a college education. In fact, up until about the mid-20th century this was seen as the primary function of higher-education. In recent decades, the attainment of an MBA has similarly come to serve as a gatekeeper to other organizations and opportunities in the business world.

In the near future, Mayo predicts that an unbiased, global perspective will be most essential to the formation of competitive networks in the modern business environment. As this progression from local interests to global interests proceeds, we may well expect network closure to accelerate linking the world into a tighter, global structure.