![Six degrees of separation](https://upload.wikimedia.org/wikipedia/commons/4/4a/Six_degrees_of_separation.svg)
The small-world experiment comprised several experiments conducted by
Stanley Milgram
Stanley Milgram (August 15, 1933 – December 20, 1984) was an American social psychologist, best known for his controversial experiments on obedience conducted in the 1960s during his professorship at Yale.Blass, T. (2004). ''The Man Who Shocke ...
and other researchers examining the
average path length Average path length, or average shortest path length is a concept in network topology that is defined as the average number of steps along the shortest paths for all possible pairs of network nodes. It is a measure of the efficiency of information ...
for
social network
A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for an ...
s of people in the United States. The research was groundbreaking in that it suggested that human society is a
small-world-type network characterized by short path-lengths. The experiments are often associated with the phrase "
six degrees of separation
Six degrees of separation is the idea that all people are six or fewer social connections away from each other. As a result, a chain of "friend of a friend" statements can be made to connect any two people in a maximum of six steps. It is also k ...
", although Milgram did not use this term himself.
Historical context of the small-world problem
Guglielmo Marconi
Guglielmo Giovanni Maria Marconi, 1st Marquis of Marconi (; 25 April 187420 July 1937) was an Italians, Italian inventor and electrical engineering, electrical engineer, known for his creation of a practical radio wave-based Wireless telegrap ...
's conjectures based on his radio work in the early 20th century, which were articulated in his 1909
Nobel Prize
The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfr ...
address, may have inspired Hungarian author
Frigyes Karinthy
Frigyes Karinthy (; 25 June 1887 – 29 August 1938) was a Hungarian author, playwright, poet, journalist, and translator. He was the first proponent of the six degrees of separation concept, in his 1929 short story, ''Chains'' (''Láncszemek'') ...
to write a challenge to find another person to whom he could not be connected through at most five people.
[Barabási, Albert-László]
. 2003.
" New York: Plume. This is perhaps the earliest reference to the concept of
six degrees of separation
Six degrees of separation is the idea that all people are six or fewer social connections away from each other. As a result, a chain of "friend of a friend" statements can be made to connect any two people in a maximum of six steps. It is also k ...
, and the search for an answer to the small world problem.
Mathematician
Manfred Kochen and political scientist
Ithiel de Sola Pool
Ithiel de Sola Pool (October 26, 1917 – March 11, 1984) was an American academic who was a widely celebrated and often controversial figure in the field of social sciences and information technology. He did significant research on technology an ...
wrote a mathematical manuscript, "Contacts and Influences", while working at the
University of Paris
, image_name = Coat of arms of the University of Paris.svg
, image_size = 150px
, caption = Coat of Arms
, latin_name = Universitas magistrorum et scholarium Parisiensis
, motto = ''Hic et ubique terrarum'' (Latin)
, mottoeng = Here and a ...
in the early 1950s, during a time when Milgram visited and collaborated in their research. Their unpublished manuscript circulated among academics for over 20 years before publication in 1978. It formally articulated the mechanics of
social network
A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for an ...
s, and explored the mathematical consequences of these (including the degree of connectedness). The manuscript left many significant questions about networks unresolved, and one of these was the number of degrees of separation in actual social networks.
Milgram took up the challenge on his return from Paris, leading to the experiments reported in "The Small World Problem" in the May 1967 (charter) issue of the popular magazine ''
Psychology Today
''Psychology Today'' is an American media organization with a focus on psychology and human behavior. It began as a bimonthly magazine, which first appeared in 1967. The ''Psychology Today'' website features therapy and health professionals direct ...
'', with a more rigorous version of the paper appearing in ''
Sociometry
Sociometry is a quantitative method for measuring social relationships. It was developed by psychotherapist Jacob L. Moreno and Helen Hall Jennings in their studies of the relationship between social structures and psychological well-being, and ...
'' two years later. The ''Psychology Today'' article generated enormous publicity for the experiments, which are well known today, long after much of the formative work has been forgotten.
Milgram's experiment was conceived in an era when a number of independent threads were converging on the idea that the world is becoming increasingly interconnected. Michael Gurevich had conducted seminal work in his empirical study of the structure of social networks in his
MIT
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...
doctoral dissertation under Pool. Mathematician Manfred Kochen, an Austrian who had been involved in
statist
In political science, statism is the doctrine that the political authority of the state is legitimate to some degree. This may include economic and social policy, especially in regard to taxation and the means of production.
While in use since ...
urban design
Urban design is an approach to the design of buildings and the spaces between them that focuses on specific design processes and outcomes. In addition to designing and shaping the physical features of towns, cities, and regional spaces, urban de ...
, extrapolated these empirical results in a mathematical manuscript, ''Contacts and Influences'', concluding that, in an American-sized population without social structure, "it is practically certain that any two individuals can contact one another by means of at least two intermediaries. In a
ociallystructured population it is less likely but still seems probable. And perhaps for the whole world's population, probably only one more bridging individual should be needed." They subsequently constructed
Monte Carlo simulation
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be determini ...
s based on Gurevich's data, which recognized that both weak and strong acquaintance links are needed to model social structure. The simulations, running on the slower computers of 1973, were limited, but still were able to predict that a more realistic three degrees of separation existed across the U.S. population, a value that foreshadowed the findings of Milgram.
Milgram revisited Gurevich's experiments in acquaintanceship networks when he conducted a highly publicized set of experiments beginning in 1967 at
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
. One of Milgram's most famous works is a study of obedience and authority, which is widely known as the Milgram Experiment. Milgram's earlier association with Pool and Kochen was the likely source of his interest in the increasing interconnectedness among human beings. Gurevich's interviews served as a basis for his small world experiments.
Milgram sought to develop an experiment that could answer the small world problem. This was the same phenomenon articulated by the writer
Frigyes Karinthy
Frigyes Karinthy (; 25 June 1887 – 29 August 1938) was a Hungarian author, playwright, poet, journalist, and translator. He was the first proponent of the six degrees of separation concept, in his 1929 short story, ''Chains'' (''Láncszemek'') ...
in the 1920s while documenting a widely circulated belief in
Budapest
Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...
that individuals were separated by six degrees of social contact. This observation, in turn, was loosely based on the seminal
demographic
Demography () is the statistical study of populations, especially human beings.
Demographic analysis examines and measures the dimensions and dynamics of populations; it can cover whole societies or groups defined by criteria such as edu ...
work of the Statists who were so influential in the design of Eastern European cities during that period. Mathematician
Benoit Mandelbrot, born in Poland and having traveled extensively in Eastern Europe, was aware of the Statist rules of thumb, and was also a colleague of Pool, Kochen and Milgram at the University of Paris during the early 1950s (Kochen brought Mandelbrot to work at the
Institute for Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
and later
IBM in the U.S.). This circle of researchers was fascinated by the interconnectedness and "social capital" of social networks.
Milgram's study results showed that people in the United States seemed to be connected by approximately three friendship links, on average, without speculating on global linkages; he never actually used the phrase "six degrees of separation". Since the ''
Psychology Today
''Psychology Today'' is an American media organization with a focus on psychology and human behavior. It began as a bimonthly magazine, which first appeared in 1967. The ''Psychology Today'' website features therapy and health professionals direct ...
'' article gave the experiments wide publicity, Milgram, Kochen, and Karinthy all had been incorrectly attributed as the origin of the notion of "six degrees"; the most likely popularizer of the phrase "six degrees of separation" is
John Guare
John Guare ( ;; born February 5, 1938) is an American playwright and screenwriter. He is best known as the author of '' The House of Blue Leaves'' and '' Six Degrees of Separation''.
Early life
He was raised in Jackson Heights, Queens.Druckman ...
, who attributed the value "six" to Marconi.
The experiment
Milgram's experiment developed out of a desire to learn more about the probability that two randomly selected people would know each other.
This is one way of looking at the small world problem. An alternative view of the problem is to imagine the population as a social network and attempt to find the
average path length Average path length, or average shortest path length is a concept in network topology that is defined as the average number of steps along the shortest paths for all possible pairs of network nodes. It is a measure of the efficiency of information ...
between any two nodes. Milgram's experiment was designed to measure these path lengths by developing a procedure to count the number of ties between any two people.
Basic procedure
![Experement Small World (possible option)](https://upload.wikimedia.org/wikipedia/commons/7/72/Experement_Small_World_%28possible_option%29.gif)
# Though the experiment went through several variations, Milgram typically chose individuals in the U.S. cities of
Omaha, Nebraska
Omaha ( ) is the largest city in the U.S. state of Nebraska and the county seat of Douglas County. Omaha is in the Midwestern United States on the Missouri River, about north of the mouth of the Platte River. The nation's 39th-largest cit ...
, and
Wichita, Kansas
Wichita ( ) is the largest city in the U.S. state of Kansas and the county seat of Sedgwick County, Kansas, Sedgwick County. As of the 2020 United States census, 2020 census, the population of the city was 397,532. The Wichita metro area had ...
, to be the starting points and
Boston, Massachusetts, to be the end point of a chain of correspondence. These cities were selected because they were thought to represent a great distance in the United States, both socially and geographically.
# Information packets were initially sent to "randomly" selected individuals in Omaha or Wichita. They included letters, which detailed the study's purpose, and basic information about a target contact person in Boston. It additionally contained a roster on which they could write their own name, as well as business reply cards that were pre-addressed to Harvard.
# Upon receiving the invitation to participate, the recipient was asked whether he or she personally knew the contact person described in the letter. If so, the person was to forward the letter directly to that person. For the purposes of this study, knowing someone "personally" was defined as knowing them on a first-name basis.
# In the more likely case that the person did not personally know the target, then the person was to think of a friend or relative who was more likely to know the target. They were then directed to sign their name on the roster and forward the packet to that person. A postcard was also mailed to the researchers at Harvard so that they could track the chain's progression toward the target.
# When and if the package eventually reached the contact person in Boston, the researchers could examine the roster to count the number of times it had been forwarded from person to person. Additionally, for packages that never reached the destination, the incoming postcards helped identify the break point in the chain.
Results
Shortly after the experiments began, letters would begin arriving to the targets and the researchers would receive postcards from the respondents. Sometimes the packet would arrive to the target in as few as one or two hops, while some chains were composed of as many as nine or ten links. However, a significant problem was that often people refused to pass the letter forward, and thus the chain never reached its destination. In one case, 232 of the 296 letters never reached the destination.
However, 64 of the letters eventually did reach the target contact. Among these chains, the
average path length Average path length, or average shortest path length is a concept in network topology that is defined as the average number of steps along the shortest paths for all possible pairs of network nodes. It is a measure of the efficiency of information ...
fell around five and a half or six. Hence, the researchers concluded that people in the United States are separated by about six people on average. Although Milgram himself never used the phrase "
six degrees of separation
Six degrees of separation is the idea that all people are six or fewer social connections away from each other. As a result, a chain of "friend of a friend" statements can be made to connect any two people in a maximum of six steps. It is also k ...
", these findings are likely to have contributed to its widespread acceptance.
In an experiment in which 160 letters were mailed out, 24 reached the target in his home in
Sharon, Massachusetts
Sharon is a New England town in Norfolk County, Massachusetts, United States. The population was 18,575 at the 2020 census. Sharon is part of Greater Boston, about southwest of downtown Boston, and is connected to both Boston and Providence by ...
. Of those 24 letters, 16 were given to the target by the same person, a clothing merchant Milgram called "Mr. Jacobs". Of those that reached the target at his office, more than half came from two other men.
The researchers used the postcards to qualitatively examine the types of chains that are created. Generally, the package quickly reached a close geographic proximity, but would circle the target almost randomly until it found the target's inner circle of friends.
This suggests that participants strongly favored geographic characteristics when choosing an appropriate next person in the chain.
Criticisms
There are a number of methodological criticisms of the small-world experiment, which suggest that the average path length might actually be smaller or larger than Milgram expected. Four such criticisms are summarized here:
# Judith Kleinfeld argues that Milgram's study suffers from selection and non-response bias due to the way participants were recruited and high non-completion rates. First, the "starters" were not chosen at random, as they were recruited through an advertisement that specifically sought people who considered themselves well-connected. Another problem has to do with the attrition rate. If one assumes a constant portion of non-response for each person in the chain, longer chains will be under-represented because it is more likely that they will encounter an unwilling participant. Hence, Milgram's experiment should underestimate the true average path length. Several methods have been suggested to correct these estimates; one uses a variant of
survival analysis
Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysi ...
in order to account for the length information of interrupted chains, and thus reduce the bias in the estimation of average degrees of separation.
[Schnettler, Sebastian. 2009. "A small world on feet of clay? A comparison of empirical small-world studies against best-practice criteria." Social Networks, 31(3), pp. 179-189, ]
# One of the key features of Milgram's methodology is that participants are asked to choose the person they know who is most likely to know the target individual. But in many cases, the participant may be unsure which of their friends is the most likely to know the target. Thus, since the participants of the Milgram experiment do not have a topological map of the social network, they might actually be sending the package further away from the target rather than sending it along the
shortest path
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
The problem of finding the shortest path between tw ...
. This is very likely to increase route length, overestimating the average number of ties needed to connect two random people. An omniscient path-planner, having access to the complete social graph of the country, would be able to choose a shortest path that is, in general, shorter than the path produced by a
greedy algorithm
A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally ...
that makes local decisions only.
# A description of heterogeneous social networks still remains an open question. Though much research was not done for a number of years, in 1998
Duncan Watts
Duncan James Watts (born February 20, 1971) 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.
...
and
Steven Strogatz
Steven Henry Strogatz (), born August 13, 1959, is an American mathematician and the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University.
He is known for his work on nonlinear systems, including contributions to the study o ...
published a breakthrough paper in the journal ''Nature.'' Mark Buchanan said, "Their paper touched off a storm of further work across many fields of science" (''Nexus'', p60, 2002). See Watts' book on the topic: ''
Six Degrees: The Science of a Connected Age''.
# Some communities, such as the
Sentinelese
The Sentinelese, also known as the Sentineli and the North Sentinel Islanders, are an indigenous people who inhabit North Sentinel Island in the Bay of Bengal in the northeastern Indian Ocean. Designated a Particularly Vulnerable Tribal Group ...
, are completely isolated, disrupting the otherwise global chains. Once these people are discovered, they remain more "distant" from the vast majority of the world, as they have few economic, familial, or social contacts with the world at large; before they are discovered, they are not within any degree of separation from the rest of the population. However, these populations are invariably tiny, rendering them of low statistical relevance.
In addition to these methodological criticisms, conceptual issues are debated. One regards the social relevance of indirect contact chains of different degrees of separation. Much formal and empirical work focuses on diffusion processes, but the literature on the small-world problem also often illustrates the relevance of the research using an example (similar to Milgram's experiment) of a targeted search in which a starting person tries to obtain some kind of resource (e.g., information) from a target person, using a number of intermediaries to reach that target person. However, there is little empirical research showing that indirect channels with a length of about six degrees of separation are actually used for such directed search, or that such search processes are more efficient compared to other means (e.g., finding information in a directory).
[Schnettler, Sebastian. 2009. "A structured overview of 50 years of small-world research" Social Networks, 31(3), pp. 165-178, ]
Influence
The social sciences
''
The Tipping Point
''The Tipping Point: How Little Things Can Make a Big Difference'' is the debut book by Malcolm Gladwell, first published by Little, Brown in 2000. Gladwell defines a tipping point as "the moment of critical mass, the threshold, the boiling po ...
'' by
Malcolm Gladwell
Malcolm Timothy Gladwell (born 3 September 1963) is an English-born Canadian journalist, author, and public speaker. He has been a staff writer for ''The New Yorker'' since 1996. He has published seven books: '' The Tipping Point: How Little T ...
, based on articles originally published in ''
The New Yorker
''The New Yorker'' is an American weekly magazine featuring journalism, commentary, criticism, essays, fiction, satire, cartoons, and poetry. Founded as a weekly in 1925, the magazine is published 47 times annually, with five of these issues ...
'', elaborates on the "funneling" concept. Gladwell condenses sociological research, which argues that the six-degrees phenomenon is dependent on a few extraordinary people ("
connectors") with large networks of contacts and friends: these hubs then mediate the connections between the vast majority of otherwise weakly connected individuals.
Recent work in the effects of the small world phenomenon on disease transmission, however, have indicated that due to the
strongly connected
In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly connected components of an arbitrary directed graph form a partition into subgraphs that ...
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
Graph may refer to:
Mathematics
*Graph (discrete mathematics), a structure made of vertices and edges
**Graph theory, the study of such graphs and their properties
*Graph (topology), a topological space resembling a graph in the sense of discre ...
(Barrett et al., 2005).
Mathematicians and actors
Smaller communities, such as mathematicians and actors, have been found to be densely connected by chains of personal or professional associations. Mathematicians have created the
Erdős number
The Erdős number () describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual ...
to describe their distance from
Paul Erdős
Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...
based on shared publications. A similar exercise has been carried out for the actor
Kevin Bacon
Kevin Norwood Bacon (born July 8, 1958) is an American actor. His films include the musical-drama film '' Footloose'' (1984), the controversial historical conspiracy legal thriller '' JFK'' (1991), the legal drama '' A Few Good Men'' (1992), t ...
and other actors who appeared in movies together with him — the latter effort informing the game "
Six Degrees of Kevin Bacon
Six Degrees of Kevin Bacon or Bacon's Law is a parlor game where players challenge each other to arbitrarily choose an actor and then connect them to another actor via a film that both actors have appeared in together, repeating this process to t ...
". There is also the combined
Erdős-Bacon number, for actor-mathematicians and mathematician-actors. Players of the popular Asian game
Go describe their distance from the great player
Honinbo Shusaku
In the history of Go in Japan, the four Go houses were four major schools of Go instituted, supported, and controlled by the state, at the beginning of the Tokugawa shogunate. (There were also many minor houses.) At roughly the same time shogi w ...
by counting their
Shusaku number, which counts degrees of separation through the games the players have had.
Current research on the small-world problem
The small-world question is still a popular research topic today, with many experiments still being conducted. For instance, Peter Dodds, Roby Muhamad, and Duncan Watts conducted the first large-scale replication of Milgram's experiment, involving 24,163 e-mail chains and 18 targets around the world.
Dodds ''et al''. also found that the mean chain length was roughly six, even after accounting for attrition. A similar experiment using popular social networking sites as a medium was carried out at
Carnegie Mellon University
Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania. One of its predecessors was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools; it became the Carnegie Institute of Technology ...
. Results showed that very few messages actually reached their destination. However, the critiques that apply to Milgram's experiment largely apply also to this current research.
Network models
In 1998,
Duncan J. Watts
Duncan James Watts (born February 20, 1971) 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.
E ...
and
Steven Strogatz
Steven Henry Strogatz (), born August 13, 1959, is an American mathematician and the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University.
He is known for his work on nonlinear systems, including contributions to the study o ...
from
Cornell University
Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...
published the first network model on the small-world phenomenon. They showed that networks from both the natural and man-made world, such as
power grid
An electrical grid is an interconnected network for electricity delivery from producers to consumers. Electrical grids vary in size and can cover whole countries or continents. It consists of:Kaplan, S. M. (2009). Smart Grid. Electrical Power ...
s and the neural network of ''
C. elegans
''Caenorhabditis elegans'' () is a free-living transparent nematode about 1 mm in length that lives in temperate soil environments. It is the type species of its genus. The name is a blend of the Greek ''caeno-'' (recent), ''rhabditis'' (r ...
'', exhibit the small-world phenomenon. Watts and Strogatz showed that, beginning with a regular lattice, the addition of a small number of random links reduces the diameter—the longest direct path between any two vertices in the network—from being very long to being very short. The research was originally inspired by Watts' efforts to understand the synchronization of
cricket
Cricket is a bat-and-ball game played between two teams of eleven players on a field at the centre of which is a pitch with a wicket at each end, each comprising two bails balanced on three stumps. The batting side scores runs by striki ...
chirps
A chirp is a signal in which the frequency increases (''up-chirp'') or decreases (''down-chirp'') with time. In some sources, the term ''chirp'' is used interchangeably with sweep signal. It is commonly applied to sonar, radar, and laser system ...
, which show a high degree of coordination over long ranges as though the insects are being guided by an invisible conductor. The mathematical model which Watts and Strogatz developed to explain this phenomenon has since been applied in a wide range of different areas. In Watts' words:
Generally, their model demonstrated the truth in
Mark Granovetter
Mark Sanford Granovetter (; born October 20, 1943) is an American sociologist and professor at Stanford University. He is best known for his work in social network theory and in economic sociology, particularly his theory on the spread of info ...
's observation that it is "the strength of weak ties"
"The Strength of Weak Ties"
'' Am J Sociol'' May 1973: Vol. 78, No. 6 pp. 1360-1380 that holds together a social network. Although the specific model has since been generalized by Jon Kleinberg
Jon Michael Kleinberg (born 1971) is an American computer scientist and the Tisch University Professor of Computer Science and Information Science at Cornell University known for his work in algorithms and networks. He is a recipient of the Nevanl ...
, it remains a canonical case study in the field of complex network
In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real s ...
s. In network theory
Network theory is the study of graphs as a representation of either symmetric relations or asymmetric relations between discrete objects. In computer science and network science, network theory is a part of graph theory: a network can be defi ...
, the idea presented in the small-world network
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 sm ...
model has been explored quite extensively. Indeed, several classic results in random graph
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs li ...
theory show that even networks with no real topological structure exhibit the small-world phenomenon, which mathematically is expressed as the diameter of the network growing with the logarithm of the number of nodes (rather than proportional to the number of nodes, as in the case for a lattice). This result similarly maps onto networks with a power-law degree distribution, such as scale-free networks
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction ''P''(''k'') of nodes in the network having ''k'' connections to other nodes goes for large values of ''k'' as
:
P(k ...
.
In computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
, the small-world phenomenon (although it is not typically called that) is used in the development of secure peer-to-peer protocols, novel routing algorithms for the Internet and ad hoc
Ad hoc is a Latin phrase meaning literally 'to this'. In English, it typically signifies a solution for a specific purpose, problem, or task rather than a generalized solution adaptable to collateral instances. (Compare with ''a priori''.)
Com ...
wireless networks, and search algorithms for communication networks of all kinds.
In popular culture
Social networks pervade popular culture in the United States and elsewhere. In particular, the notion of six degrees has become part of the collective consciousness. Social networking service
A social networking service or SNS (sometimes called a social networking site) is an online platform which people use to build social networks or social relationships with other people who share similar personal or career content, interests, act ...
s such as Facebook
Facebook is an online social media and social networking service owned by American company Meta Platforms. Founded in 2004 by Mark Zuckerberg with fellow Harvard College students and roommates Eduardo Saverin, Andrew McCollum, Dustin M ...
, Linkedin, and Instagram have greatly increased the connectivity of the online space through the application of social networking concepts.
See also
*
*
*
*
*
*
*
*
*
References
External links
Planetary-Scale Views on an Instant-Messaging Network
*Theory tested for specific groups:
*
The Oracle of Bacon at Virginia
*
The Oracle of Baseball
*
The Erdős Number Project
*
The Oracle of Music
*
CoverTrek - linking bands and musicians via cover versions
*
** – article published in Defense Acquisition University
The Defense Acquisition University (DAU) is a corporate university of the United States Department of Defense offering "acquisition, technology, and logistics" (AT&L) training to military and Federal civilian staff and Federal contractors. DAU is ...
's journal ''Defense AT&L'', proposing "small world / large tent" social networking model
{{DEFAULTSORT:Small World Experiment
Community building
Psychology experiments
Social network analysis