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Topic: Small world phenomenon


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  Small world phenomenon - Wikipedia, the free encyclopedia
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.
In his first "small world" experiment, documented in an undated paper entitled "Results of Communication Project," Milgram sent 60 letters to various recruits in Omaha, Nebraska who were asked to forward the letter to a stockbroker living at a specified location in Sharon, Massachusetts.
Recent work in the effects of the small world phenomenon on disease transmission, however, have indicated that due to the strongly-connected nature of social networks as a whole, removing these hubs from a population usually has little effect on the average path length through the graph (Barrett et al., 2005).
en.wikipedia.org /wiki/Small_world_phenomenon   (1333 words)

  
 Small World
The biological world turns out to be a remarkably small one, with the predator-prey links between species arranged in such a way that no species is more than a handful of steps away from any other.
In the social setting, the "small world" experience is closely linked to the notion of "six degrees of separation" - the idea that each of us is linked to everyone else on the planet by a chain of no more than six intermediary acquaintances.
If healthy ecosystems are small worlds characterised by a few hub species, with a preponderance of weak links providing their stability, then the global depletion of species numbers is truly alarming.
flatrock.org.nz /topics/science/small_world.htm   (5534 words)

  
 Could It Be A Big World After All?
Despite the explosion of scholarly and media interest, the small world problem has dropped out of the discipline of psychology, a discipline especially suited to examining the cognitive and emotional questions that the mathematicians are identifying.
I fantasized about finding the original target people in Milgram's small world studies--- such as the Boston stockbroker or even his children--- and asking them to be the targets for this replication more than a quarter of a century later, a bit of showmanship worthy of Stanley Milgram himself.
While the small world problem is rarely covered in introductory psychology textbooks and has been the topic of little recent psychological research, an explosion of interest in this fascinating issue is occurring in mathematics and other fields.
www.uaf.edu /northern/big_world.html   (4138 words)

  
 Wikinfo | Small world phenomenon   (Site not responding. Last check: 2007-10-31)
In his first "small world" experiment (documented in an undated paper entitled "Results of Communication Project"), Milgram sent 60 letters to various recruits in Wichita, Kansas who were asked to forward the letter to the wife of a divinity student living at a specified location in Cambridge, Massachusetts.
If there was some doubt as to whether the "whole world" was a small world, there was very little doubt that there were a large number of small worlds within that whole (from faculty chains at Michigan State University to a close-knit Jewish community in Montreal).
For those chains that did reach completion the number 6 emerged as the mean number of intermediaries and thus the expression "six degrees of separation" (perhaps by analogy to "six degrees of freedom") was born.
www.wikinfo.org /wiki.php?title=Small_world_phenomenon   (1069 words)

  
 big_world.html
Milgram's own empirical findings on the small world problem do not justify his famous conclusion---that we live in a "small world" where people are connected, on the average, by "six degrees of separation." Milgram's first unpublished study and unpublished attempts at replication, available in the Milgram papers, show the weakness of the evidentiary base.
Taken as a whole, small world studies suggest we live in neither of the two worlds about which Milgram theorizes: 1) a small world, where people are connected, or 2) a big world, where people are alienated from each other, each confined to their own circles.
The "small world problem" that de Sola Pool and Stanley Milgram were investigating does not have the same mathematical structure as the "small world experiences" that people delighted in telling.
www.columbia.edu /itc/sociology/watts/w3233/client_edit/big_world.html   (7323 words)

  
 Duncan Watts: "Networks, Dynamics, and the Small-World Phenomenon"
Abstract: The small-world phenomenon formalized in this article as the coincidence of high local clustering and short global separation, is shown to...
The small-world phenomenon formalized in this article as the coincidence of high local clustering and short global separation, is shown to be a general feature of sparse, decentralized networks that are neither completely ordered nor completely random.
Furthermore, small admixtures of randomness to an otherwise ordered network can have a dramatic impact on its dynamical, as well as structural, properties - a feature illustrated by a simple model of disease transmission.
www.zephoria.org /alterity/archives/2005/09/duncan_watts__n.html   (576 words)

  
 Sacramento State Bulletin
There may be six degrees of separation out in the larger world, but on the Sacramento State campus a researcher and her students have found that there can be fewer than three degrees of separation among the thousands of people here—making a big university seem much smaller and friendlier than might be expected.
She said that key to the structure of the small world phenomenon are individuals who Tom calls “mavens,” persons with a great deal of influence in social networks and who serve as multipliers who pass on information to others.
Tom said the results of her study suggest that the small world phenomenon is instrumental in the development of connectedness among diverse social groups on campus.
www.csus.edu /bulletin/bulletin012306/bulletin012306smallworld.htm   (615 words)

  
 Small World Experiment
Furthermore, according to unpublished research by Judith Kleinfeld, based on her survey of Milgram's original notes in the Yale archives, data that Milgram did not publish (on the Kansas study) did not support his hypothesis.
either as equally small or smaller (in terms of number of participants), or else as highly restricted contextually (such as within a single university).
In this project, we intend to perform the first large scale, global verification of the small world hypothesis, using the modern Email equivalent of Milgram's passport innovation.
smallworld.columbia.edu /description.html   (597 words)

  
 Amazon.co.uk: Small World: Uncovering Nature's Hidden Networks: Books: Mark Buchanan   (Site not responding. Last check: 2007-10-31)
Whenever coincidence prompts to say that "it's a small world", we have, says Buchanan, stumbled upon a piece of mathematics as fundamental to the natural world as Fibonacci numbers and the Golden Mean.
Buchanan has been quick off the mark with this book: the mature study of small world networks is barely four years old; so, naturally enough, the same pioneering names recur often as he outlines the field's development.
Buchanan points out the hidden networks that tie together both the physical world and the world of consciousness, showing that amongst other things the Internet, electrical grids, the brain and the global economy are all systems with an underlying pattern that shares nature's design.
www.amazon.co.uk /Small-World-Uncovering-Natures-Networks/dp/0297607421   (1862 words)

  
 CiteULike: Economic Small-World Behavior in Weighted Networks   (Site not responding. Last check: 2007-10-31)
The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems.
The combination of these factors leads us to introduce the concept of <em> economic small worlds</em>, that formalizes the idea of networks that are "cheap" to build, and nevertheless efficient in propagating information, both at global and local scale.
The combination of these factors leads us to introduce the concept of economic small worlds, that formalizes the idea of networks that are "cheap" to build, and nevertheless efficient in propagating information, both at global and local scale.
www.citeulike.org /user/BenediktM/article/692517   (628 words)

  
 NetLogo Models Library: Small Worlds
This model explores the formation of networks that result in the "small world" phenomenon -- the idea that a person is only a couple of connections away any other person in the world.
To identify small worlds, the "average path length" (abbreviated "apl") and "clustering coefficient" (abbreviated "cc") of the network are calculated and plotted after the REWIRE-ONCE or REWIRE-ALL buttons are pressed.
Clustering Coefficient: Another property of small world networks is that from one person's perspective it seems unlikely that they could be only a few steps away from anybody else in the world.
ccl.northwestern.edu /netlogo/models/SmallWorlds   (1336 words)

  
 Explaining the "Small World" Phenomenon
The world is tied together by a network of personal relationships, and often we're impressed by how tightly these connections work.
But two Cornell University mathematicians have now shown that small worlds are probably common in many networks found in nature and are easy to create in systems as diverse as networks of people, power grids and the neurons in the human brain.
They also applied the analysis to a model for the spread of an infectious disease through a population and found that disease would spread almost as quickly through a "small world" as through a world in which everyone was connected at random.
www.unc.edu /depts/cmse/math/smallworld.html   (1005 words)

  
 The Small-World Phenomenon: An Algorithmic Perspective - Kleinberg (ResearchIndex)   (Site not responding. Last check: 2007-10-31)
Abstract: Long a matter of folklore, the "small-world phenomenon" -- the principle that we are all linked by short chains of acquaintances -- was inaugurated as an area of experimental study in the social sciences through the pioneering work of Stanley Milgram in the 1960's.
This work was among the first to make the phenomenon quantitative, allowing people to speak of the "six degrees of separation" between any two people in the United States.
14 The Small World (context) - Kochen - 1989
citeseer.ist.psu.edu /kleinberg00smallworld.html   (597 words)

  
 Amazon.com: Small World: Books: David Lodge   (Site not responding. Last check: 2007-10-31)
Small World is sort of a sequel to Nice Work (it has some of the same characters and locations, but doesn't rely on knowledge of its predecessor).
Small World is also a satire on academia, and while all the jacket blurbs talk about how biting the satire is, I didn't find that to be the case.
Small World is the second installment of a trilogy.
www.amazon.com /Small-World-David-Lodge/dp/0140244867   (2173 words)

  
 It’s a small world, after all - Aetiology
Similarly, Duncan Watts first became interested in the “small world problem”—the idea that all of us are more closely connected than we realize—after watching fireflies flash in synchrony, and wondering how they accomplished that.
At the base of this phenomenon in infectious diseases is an idea called the "tipping point." This is something epidemiologists have discussed much in recent months regarding the potential of an avian influenza pandemic—tiny influences can have startling effects.
What we see when we examine this graphically is a "small world" network: a series of hubs and connectors, with the largest hubs—-termed "superspreaders" (the numbered dots in the picture above)--responsible for a disproportionately large number of secondary cases.
aetiology.blogspot.com /2005/11/its-small-world-after-all.html   (1548 words)

  
 Small World Networks
The small-world phenomenon is a generalized version of this experience, the claim being that even when two people do not have a friend in common, only a short chain of intermediaries separates them.
What this research suggests is that the small-world phenomenon may be common for many large networks found in nature; it is not merely an artifact of an idealized model.
Another aspect of the phenomenon will be studied in a working group organized by Charles Sabel on using the intuitions from small-world dynamics to increase the effectiveness of organizations solving complex problems in rapidly changing environments.
mysite.verizon.net /pulsar/Library_Ref/Business/Marketing/6degreesSeparation/smallWorld_Network.html   (3082 words)

  
 Small world phenomenon (via CobWeb/3.1 planetlab-1.cs.princeton.edu)   (Site not responding. Last check: 2007-10-31)
The concept gave rise to the famous phrase six degrees of separation after a 1967 small world experiment by psychologist Stanley Milgram which found that two random US citizens were connected by an average of six acquaintances.
While Watts' model was able to explain the high clustering coefficient and the short average path length of a small world, it lacked an explanation for another property found in real-world networks such as the Internet: these networks are scale-free.
It appears that the scale-free network model may be the foundation for a law of nature which governs the formation of natural small world networks.
small-world-phenomenon.kiwiki.homeip.net.cob-web.org:8888   (1388 words)

  
 smallworld
Viewed in computational terms, this is a statement about the power of a routing algorithm, equipped with purely local information, to find efficient paths to a destination; that such a decentralized routing scheme is effective says something striking about the underlying social network.
The ability to construct a searchable network in this way, with long-range links whose probabilities decay with distance, has proved useful in the design of peer-to-peer file-sharing systems on the Internet, where content must be found by nodes consulting one another in a decentralized fashion.
In other words, nodes executing these look-up protocols are behaving very much like participants in the Milgram experiments---a striking illustration of the way in which the computational and social sciences can inform one another, and the way in which mathematical models in the computational world turn into design principles with remarkable ease.
www.siam.org /siamnews/04-04/smallworld.htm   (650 words)

  
 Amazon.fr : Small Worlds: The Dynamics of Networks Between Order and Randomness: Livres en anglais: Duncan J. Watts   (Site not responding. Last check: 2007-10-31)
Everyone knows the small-world phenomenon: soon after meeting a stranger, we are surprised to discover that we have a mutual friend, or we are connected through a short chain of acquaintances.
The networks of this story are everywhere: the brain is a network of neurons; organisations are people networks; the global economy is a network of national economies, which are networks of markets, which are in turn networks of interacting producers and consumers.
Many of these networks, the author claims, will turn out to be small worlds.
www.amazon.fr /Small-Worlds-Dynamics-Networks-Randomness/dp/0691117047   (513 words)

  
 Seminar: Small world networks and applications to bioinformatics   (Site not responding. Last check: 2007-10-31)
The small world phenomenon -- high local clustering coupled with relatively small average pathlengths -- has been observed in many real life networks.
This is directly observed and also a logical consequence of the size of the genome(s) when considered in relation to the plethora of such functions.
I will show that reverse engineering a small world graph from a biological dataset presents a number of mathematical and computational challenges.
www.kingston.ac.uk /maths/seminars/abstract.php?id=7   (226 words)

  
 Small World Network -- from Wolfram MathWorld
This is known as the small world phenomenon.
It is sometimes also known as "six degrees of separation" since, in the social network of the world, any person turns out to be linked to any other person by roughly six connections.
In modern mathematics, the center of the network of coauthorship is considered to be P. Erdos, resulting in the so-called Erdos number.
mathworld.wolfram.com /SmallWorldNetwork.html   (238 words)

  
 Small world - Wikipedia, the free encyclopedia
Small World, a comic novel by the British author David Lodge.
"it's a small world", an attraction at several of the Disney theme parks.
The small world phenomenon, which is the theory that everyone in the world can be reached through a short chain of social acquaintances.
en.wikipedia.org /wiki/Small_world   (157 words)

  
 The Small-World Phenomenon: An Algorithmic Perspective 1
Long a matter of folklore, the ``small-world phenomenon'' -- the principle that we are all linked by short chains of acquaintances -- was inaugurated as an area of experimental study in the social sciences through the pioneering work of Stanley Milgram in the 1960's.
One of the most refined of these models was formulated in recent work of Watts and Strogatz; their framework provided compelling evidence that the small-world phenomenon is pervasive in a range of networks arising in nature and technology, and a fundamental ingredient in the evolution of the World Wide Web.
One then introduces a small number of edges in which the endpoints are chosen uniformly at random from V -- the ``long-range contacts''.
www.cs.cornell.edu /home/kleinber/swn.d/swn.html   (5001 words)

  
 Complex Networks
This result relies on the fact that the crossover from large to small worlds is obtained with only a small but finite fraction of rewired links.
For the case of the airport network we have access to data on number of passengers in transit and of cargo leaving or arriving at the airport, instead of data on the number of distinct connections.
This effect is exemplified by the network of world airports: for reasons of efficiency, commercial airlines prefer to have a small number of hubs where all routes would connect.
polymer.bu.edu /~amaral/Content_network.html   (2006 words)

  
 Essay: The Small-World Phenomenon and Decentralized Search
The small-world phenomenon -- the principle that we are all linked by short chains of acquaintances, or "six degrees of separation" -- is a fundamental issue in social networks; it is a basic statement about the abundance of short paths in a graph whose nodes are people, with links joining pairs who know one another.
It is also a topic on which the feedback between social, mathematical, and computational issues has been particularly fluid.
In other words, nodes executing these look-up protocols are behaving very much like participants in the Milgram experiments -- a striking illustration of the way in which the computational and social sciences can inform one another, and the way in which mathematical models in the computational world turn into design principles with remarkable ease.
www.mathaware.org /mam/04/essays/smallworld.html   (695 words)

  
 Small World Theory   (Site not responding. Last check: 2007-10-31)
Small World: Uncovering Nature's Hidden Networks, Buchanan, M. Random Graph Models of Social Networks, Newman, M. et al.
Model of the Small World a Review, Newman, M. Networks, Dynamics and the small-world phenomenon, Watts, D. Collective Dynamics of Small World Networks, Watts, D. et al.
Small World Phenomena and the Dynamics of Information, Kleinberg, J. Navigation in a Small World, Kleinberg, J. Small World Phenomenon an Algorithmic Perspective, Kleinberg, J. The small world web.
www.cis.strath.ac.uk /~rjg/Research/SmallWorld/index.shtml   (125 words)

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