Hong Qi

Strong and Weak Ties In the late 1960s, Mark Granovetter interviewed dozens of managerial and professional workers, asking them who helped them find their current job. Was it a friend? He kept getting the same reply: No, it was not a friend. It was just an acquaintance. Today Granovetter’s paper, The Strength of Weak Ties, is recognized as one of the most influential sociology papers ever written.

Strong and Weak Ties In The Strength of Weak Ties Granovetter proposed something that sounds preposterous at first: When it comes to finding a job, getting news, launching a restaurant, or spreading the latest fad, our weak social ties are more important than our cherished strong friendships.

Strong and Weak Ties In Mark Granovetter’s social world, society is structured into highly connected clusters, or close-knit circles of friends, in which everybody knows everybody else. Strong ties are your family, friends and other people you have strong bonds to. Weak ties are relationships that transcend local relationship boundaries both socially and geographically. Weak ties are more useful than strong ties

Strong and Weak Ties Weak ties play a crucial role in our ability to communicate with the outside world. To get new information, we have to activate our weak ties.

Erdős Number Number of links required to connect scholars to Erdős, via co-authorship of papers Erdős wrote papers with 507 co- authors.

Erdős Number Erdos has Erdos number zero. Those who coauthored a paper with him have Erdos number one. Those who wrote a paper with an Erdos coauthor have Erdos number two, and so on. The very existence of the Erdos number demonstrates that the scientists are linked to each other through the papers they written.

Erdős Number The smallness of most Erdos number indicated that this web of science truly is a small world. As it only rarely happens that the authors of a publication do not personally know each other, coauthorships represent strong social link.

Clustering Coefficient Watts and Strogatz introduced a quantity called the clustering coefficient. The clustering coefficient tells you how closely knit your circle of friends is. A number close to 1.0 means that all your friends are good friends with each other. On the other hand, if the clustering coefficient is zero, then you are the only person who holds your friends together, as they do not seem to enjoy each other’s company.

Clustering Coefficient Clustering measures the fraction of neighbors of a node that are connected themselves Regular Graphs have a high clustering coefficient but also a high diameter Random Graphs have a low clustering coefficient but a low diameter Both models do match the properties expected from real networks!

Clustering Coefficient The surprising finding of Watts and Strogatz is that even a few extra links are sufficient to drastically decrease the average separation between the nodes. These few links will not significantly change the clustering coefficient.

Hubs and connectors Goriola Dawodu

Hubs and connectors: are the ubiquitous, a building block of our complex, interconnected world.

Malcom Gladwell’s (staff writer at New Yorker magazine) test: measures how social you are Gives a list of 248 surnames complied from Manhattan phone book and ask you to give yourself a point if you know anybody with that name, if you know 3 people with the same surname on the list, you earn 3 point The list was run in a college in Manhattan : an average score of 21 was recorded A group of highly educated academics scored 39 In college class, the score ranged from 2 -99,in a random sample, the low score was 9 and the high score was 118 For highly homogenous group of people with similar age, education and income the range was enormous. The lowest score was 16 while the highest score was 108

Conclusion: “sprinkled among every walk of like…… are a handful of people with a truly extraordinary knack of making friend and quaintances. They are connectors.”

Fact about connectors Fundamental properties of most network Nodes with anomalously large numbers of links Present within the economy and within cells Important component of social network Create trends and fashion Make important deals, spread fads, or help launch a restaurant

Cyberspace An ultimate forum for democracy where everybody’s voice can be heard with equal opportunity. Content are hard to censor, once they are posted they are instantaneously available to hundreds of millions of people around the world with internet connection The more incoming link pointing to your webpage,the more visible it is

Just as in a society, a few connectors know an usually large number of people---- large architects of the World Wide Web (www) is dominated by a few very highly connected nodes or hubs Cyber Hub includes Amazon, yahoo, hotmail etc Hubs are website to which everyone links Hubs are the strongest argument against utopian vision of an egalitarian cyberspace These hubs are visible everywhere and also other link point to them

In the network behind the web many unpopular or seldom noticed nodes with only a small number of links are held together by these few highly connected sites

Student from colleges saw Kevin Bacon’s movie on air, they tried to prove that Bacon is a God by proving to the audience that Bacon had played in so many movie that could connect him to just about any actor in Hollywood The proof showed that Bacon is no closer to the center of Hollywood than to the center of the universe It was observed that every actor in Hollywood could be connected to Bacon with typically two to three links.

Two computer science students realized that determining the distance between two actors is viable computer science project. ---The two students did not watch the Bacon movie They created an oracle database ( On the website, if you type in the name of two actors in milliseconds it provided the shortest path between them, listing the chains of actors and movies through which they are connected This was possible because Hollywood forma densely interconnected network in which nodes are actors linked by movies in which they have appeared

Observation An actor has link to all other actors Those who have played in several movies linked quickly Each actors have an average of 27 links,many more than the necessary one to make the network fully connected Each actors can be connected to another actor through three links on average Six degree is unavoidable 41 percent of the actors have fewer than ten links Removing a few actors reduced the length of path to other actors The more movies an actor plays the shorter his or her average distance to his or her peer

It was found that actors with more movies failed to give the most connected actors This indicates that when it comes to network the size does not always matter. Despite the number of movies porn stars make, they fail to be anywhere near the center of Hollywood Also, Bacon was a prominent Hollywood actor who has played over forty-six movie, collecting link to more than 1,800 actors. His average separation from everyone else in Hollywood was 2.79 The actor (Rod steiger) with the closest separation had a separation of 2.53 Bacon was not only far from the universe but also far from Hollywood

Conclusion: As networks are clustered, nodes that are linked only to nodes in their cluster could have a central role in that subculture or genre

Random universe A random universe does not support connectors. If the society were random, then the Gladwell modest social sample of 400 people, with their average of around 39 social link, the most social person should have a far fewer acquaintances than 118 found. If the web were a random network, the probability of there being a page with five hundred incoming link will be practically zero (i.e. Hubs are forbidden in randomly linked web).

The average separation between two randomly selected people on the earth is six The distance between anybody and a connector is often only 1 or t2 Two pages on the web are 19 clicks away Yahoo.com, a giant hub, is reachable from most WebPages in 2 or 3 click The Hub makes the world indeed tiny